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Coulomb's law
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Coulomb's law, or Coulomb's inverse-square law, is a law of physics for quantifying the amount of force with which stationary electrically charged particles repel or attract each other. In its scalar form, the law is:
F = k e q 1 q 2 r 2 {\displaystyle F=k_{e}{\frac {q_{1}q_{2}}{r^{2}}}} ,
where ke is Coulomb's constant (ke = 7009900000000000000♠9.0×109 N m2 C−2), q1 and q2 are the signed magnitudes of the charges, and the scalar r is the distance between the charges. The force of the interaction between the charges is attractive if the charges have opposite signs (i.e., F is negative) and repulsive if like-signed (i.e., F is positive).
The law was first published in 1784 by French physicist Charles-Augustin de Coulomb and was essential to the development of the theory of electromagnetism. Being an inverse-square law, it is analogous to Isaac Newton's inverse-square law of universal gravitation. Coulomb's law can be used to derive Gauss's law, and vice versa. The law has been tested extensively, and all observations have upheld the law's principle.
Contents
[hide]
1 History
2 The law
2.1 Units
2.2 Electric field
2.3 Coulomb's constant
2.4 Limitations
2.5 Quantum Field Theory origin
3 Scalar form
4 Vector form
4.1 System of discrete charges
4.2 Continuous charge distribution
5 Simple experiment to verify Coulomb's law
6 Atomic forces
7 See also
8 Notes
9 References
10 External links
History[edit]
Charles-Augustin de Coulomb
Ancient cultures around the Mediterranean knew that certain objects, such as rods of amber, could be rubbed with cat's fur to attract light objects like feathers. Thales of Miletus made a series of observations on static electricity around 600 BC, from which he believed that friction rendered amber magnetic, in contrast to minerals such as magnetite, which needed no rubbing.[1][2] Thales was incorrect in believing the attraction was due to a magnetic effect, but later science would prove a link between magnetism and electricity. Electricity would remain little more than an intellectual curiosity for millennia until 1600, when the English scientist William Gilbert made a careful study of electricity and magnetism, distinguishing the lodestone effect from static electricity produced by rubbing amber.[1] He coined the New Latin word electricus ("of amber" or "like amber", from ἤλεκτρον [elektron], the Greek word for "amber") to refer to the property of attracting small objects after being rubbed.[3] This association gave rise to the English words "electric" and "electricity", which made their first appearance in print in Thomas Browne's Pseudodoxia Epidemica of 1646.[4]
Early investigators of the 18th century who suspected that the electrical force diminished with distance as the force of gravity did (i.e., as the inverse square of the distance) included Daniel Bernoulli[5] and Alessandro Volta, both of whom measured the force between plates of a capacitor, and Franz Aepinus who supposed the inverse-square law in 1758.[6]
Based on experiments with electrically charged spheres, Joseph Priestley of England was among the first to propose that electrical force followed an inverse-square law, similar to Newton's law of universal gravitation. However, he did not generalize or elaborate on this.[7] In 1767, he conjectured that the force between charges varied as the inverse square of the distance.[8][9]
Coulomb's torsion balance
In 1769, Scottish physicist John Robison announced that, according to his measurements, the force of repulsion between two spheres with charges of the same sign varied as x−2.06.[10]
In the early 1770s, the dependence of the force between charged bodies upon both distance and charge had already been discovered, but not published, by Henry Cavendish of England.[11]
Finally, in 1785, the French physicist Charles-Augustin de Coulomb published his first three reports of electricity and magnetism where he stated his law. This publication was essential to the development of the theory of electromagnetism.[12] He used a torsion balance to study the repulsion and attraction forces of charged particles, and determined that the magnitude of the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
The torsion balance consists of a bar suspended from its middle by a thin fiber. The fiber acts as a very weak torsion spring. In Coulomb's experiment, the torsion balance was an insulating rod with a metal-coated ball attached to one end, suspended by a silk thread. The ball was charged with a known charge of static electricity, and a second charged ball of the same polarity was brought near it. The two charged balls repelled one another, twisting the fiber through a certain angle, which could be read from a scale on the instrument. By knowing how much force it took to twist the fiber through a given angle, Coulomb was able to calculate the force between the balls and derive his inverse-square proportionality law.
The law[edit]
Coulomb's law states that:
The magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them.[12]
The force is along the straight line joining them. If the two charges have the same sign, the electrostatic force between them is repulsive; if they have different signs, the force between them is attractive.
Coulomb's law can also be stated as a simple mathematical expression. The scalar and vector forms of the mathematical equation are
| F | = k e | q 1 q 2 | r 2 {\displaystyle |\mathbf {F} |=k_{e}{|q_{1}q_{2}| \over r^{2}}\qquad } and F 1 = k e q 1 q 2 | r 21 | 2 r ^ 21 , {\displaystyle \qquad \mathbf {F} _{1}=k_{e}{\frac {q_{1}q_{2}}{{|\mathbf {r} _{21}|}^{2}}}\mathbf {\hat {r}} _{21},\qquad } respectively,
where ke is Coulomb's constant (ke = 7009898755178736817♠8.9875517873681764×109 N m2 C−2), q1 and q2 are the signed magnitudes of the charges, the scalar r is the distance between the charges, the vector r21 = r1 − r2 is the vectorial distance between the charges, and r̂21 = r21/|r21| (a unit vector pointing from q2 to q1). The vector form of the equation calculates the force F1 applied on q1 by q2. If r12 is used instead, then the effect on q2 can be found. It can be also calculated using Newton's third law: F2 = −F1.
Units[edit]
When the electromagnetic theory is expressed using the International System of Units, force is measured in newtons, charge in coulombs, and distance in metres. Coulomb's constant is given by ke = 1⁄4πε0. The constant ε0 is the electric constant (also known as "the absolute permittivity of free space") in C2 m−2 N−1. It should not be confused with εr, which is the dimensionless relative permittivity of the material in which the charges are immersed, or with their product εa = ε0εr , which is called "absolute permittivity of the material" and is still used in electrical engineering.
The SI derived units for the electric field are volts per meter, newtons per coulomb, or tesla meters per second.
Coulomb's law and Coulomb's constant can also be interpreted in various terms:
Atomic units. In atomic units the force is expressed in hartrees per Bohr radius, the charge in terms of the elementary charge, and the distances in terms of the Bohr radius.
Electrostatic units or Gaussian units. In electrostatic units and Gaussian units, the unit charge (esu or statcoulomb) is defined in such a way that the Coulomb constant k disappears because it has the value of one and becomes dimensionless.
Lorentz–Heaviside units (also called rationalized). In Lorentz–Heaviside units the Coulomb constant is ke = 1/4π and becomes dimensionless.
Gaussian units and Lorentz–Heaviside units, both of which are CGS unit systems, are often preferred in the treatment of electromagnetism as they greatly simplify formulas.[13]
Electric field[edit]
If two charges have the same sign, the electrostatic force between them is repulsive; if they have different sign, the force between them is attractive.
An electric field is a vector field that associates to each point in space the Coulomb force experienced by a test charge. In the simplest case, the field is considered to be generated solely by a single source point charge. The strength and direction of the Coulomb force F on a test charge qt depends on the electric field E that it finds itself in, such that F = qtE. If the field is generated by a positive source point charge q, the direction of the electric field points along lines directed radially outwards from it, i.e. in the direction that a positive point test charge qt would move if placed in the field. For a negative point source charge, the direction is radially inwards.
The magnitude of the electric field E can be derived from Coulomb's law. By choosing one of the point charges to be the source, and the other to be the test charge, it follows from Coulomb's law that the magnitude of the electric field E created by a single source point charge q at a certain distance from it r in vacuum is given by:
| E | = 1 4 π ε 0 | q | r 2 {\displaystyle |{\boldsymbol {E}}|={1 \over 4\pi \varepsilon _{0}}{|q| \over r^{2}}}
Coulomb's constant[edit]
Main article: Coulomb's constant
Coulomb's constant is a proportionality factor that appears in Coulomb's law as well as in other electric-related formulas. Denoted ke, it is also called the electric force constant or electrostatic constant, hence the subscript e.
The exact value of Coulomb's constant is:
k e = 1 4 π ε 0 = c 0 2 μ 0 4 π = c 0 2 × 10 − 7 H ⋅ m − 1 = 8.987 551 787 368 176 4 × 10 9 N ⋅ m 2 ⋅ C − 2 {\displaystyle {\begin{aligned}k_{e}&={\frac {1}{4\pi \varepsilon _{0}}}={\frac {c_{0}^{2}\mu _{0}}{4\pi }}=c_{0}^{2}\times 10^{-7}\ \mathrm {H\cdot m} ^{-1}\\&=8.987\,551\,787\,368\,176\,4\times 10^{9}\ \mathrm {N\cdot m^{2}\cdot C} ^{-2}\end{aligned}}}
Limitations[edit]
There are three conditions to be fulfilled for the validity of Coulomb's law:
The charges must have a spherically symmetric distribution (e.g. be point charges, or a charged metal sphere).
The charges must not overlap (e.g. they must be distinct point charges).
The charges must be stationary with respect to each other.
The last of these is the most important - it is known as the electrostatic approximation. When movement takes place, Einstein's theory of relativity must be taken into consideration, and a result, an extra factor is introduced, which alters the force produced on the two objects. This extra part of the force is called the magnetic force, and is described by magnetic fields. For slow movement, the magnetic force is minimal and Coulomb's law can still be considered approximately correct, but when the charges are moving more quickly in relation to each other, the full electrodynamic rules (incorporating the magnetic force) must be considered.
Quantum Field Theory origin[edit]
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The most basic Feynman diagram for QED interaction between two fermions
In simple terms, the Coulomb potential derives from the QED Lagrangian as follows. The Lagrangian of quantum electrodynamics is normally written in natural units, but in SI units, it is:
L Q E D = ψ ¯ ( i ℏ c γ μ D μ − m c 2 ) ψ − 1 4 ℏ c F μ ν F μ ν {\displaystyle {\mathcal {L}}_{\mathrm {QED} }={\bar {\psi }}(i\hbar c\gamma ^{\mu }D_{\mu }-mc^{2})\psi -{\frac {1}{4\hbar c}}F_{\mu \nu }F^{\mu \nu }}
where the covariant derivative (in SI units) is:
D μ = ∂ μ + i g ℏ c A μ {\displaystyle {D}_{\mu }=\partial _{\mu }+{\frac {ig}{\hbar c}}A_{\mu }}
where g {\displaystyle g} is the gauge coupling parameter. By putting the covariant derivative into the lagrangian explicitly, the interaction term (the term involving both A {\displaystyle A} and ψ {\displaystyle \psi } ) is seen to be:
L i n t = i g ψ ¯ γ μ A μ ψ {\displaystyle {\mathcal {L}}_{\mathrm {int} }=ig{\bar {\psi }}\gamma ^{\mu }A_{\mu }\psi }
The most basic Feynman diagram for a QED interaction between two fermions is the exchange of a single photon, with no loops. Following the Feynman rules, this therefore contributes two QED vertex factors ( i g Q γ μ {\displaystyle igQ\gamma _{\mu }} ) to the potential, where Q is the QED-charge operator (Q gives the charge in terms of the electron charge, and hence is exactly -1 for electrons, etc.). For the photon in the diagramme, the Feynman rules demand the contribution of one bosonic massless propagator ( ℏ c k 2 {\displaystyle {\frac {\hbar c}{k^{2}}}} ). Ignoring the momentum on the external legs (the fermions), the potential is therefore:
V ( r ) = 1 ( 2 π ) 3 ∫ e ( i k ⋅ r ℏ ) ( i Q 1 g 2 γ μ ) ( i Q 2 g 2 γ ν ) ( ℏ c k 2 ) d 3 k {\displaystyle V(\mathbf {r} )={\frac {1}{(2\pi )^{3}}}\int e^{({\frac {i\mathbf {k\cdot r} }{\hbar }})}(iQ_{1}g^{2}\gamma _{\mu })(iQ_{2}g^{2}\gamma _{\nu })({\frac {\hbar c}{k^{2}}})\;d^{3}k}
which can be more usefully written as
V ( r ) = − g 2 ℏ c Q 1 Q 2 4 π 1 ( 2 π ) 3 ∫ e ( i k ⋅ r ℏ ) 4 π η μ ν k 2 d 3 k {\displaystyle V(\mathbf {r} )={\frac {-g^{2}\hbar cQ_{1}Q_{2}}{4\pi }}{\frac {1}{(2\pi )^{3}}}\int e^{({\frac {i\mathbf {k\cdot r} }{\hbar }})}{\frac {4\pi \eta _{\mu \nu }}{k^{2}}}\;d^{3}k}
Where Q i {\displaystyle Q_{i}} is the QED-charge on the ith particle. Recognising the integral as just being a Fourier transform enables the equation to be simplified:
V ( r ) = − g 2 ℏ c Q 1 Q 2 4 π 1 r {\displaystyle V(\mathbf {r} )={\frac {-g^{2}\hbar cQ_{1}Q_{2}}{4\pi }}{\frac {1}{r}}}
For various reasons, it is more convenient to define the fine-structure constant α = g 2 4 π {\displaystyle \alpha ={\frac {g^{2}}{4\pi }}} , and then define e = 4 π α ε 0 ℏ c {\displaystyle e={\sqrt {4\pi \alpha \varepsilon _{0}\hbar c}}} . Re-arranging these definitions gives:
g 2 ℏ c = e 2 ε 0 {\displaystyle g^{2}\hbar c={\frac {e^{2}}{\varepsilon _{0}}}}
It is worth noting that g = e {\displaystyle g=e} in natural units (since, in those units, ℏ = 1 {\displaystyle \hbar =1} , c = 1 {\displaystyle c=1} , and ε 0 = 1 {\displaystyle \varepsilon _{0}=1} ). Continuing in SI units, the potential is therefore
V ( r ) = − e 2 4 π ε 0 Q 1 Q 2 r {\displaystyle V(\mathbf {r} )={\frac {-e^{2}}{4\pi \varepsilon _{0}}}{\frac {Q_{1}Q_{2}}{r}}}
Defining q i = e Q i {\displaystyle q_{i}=eQ_{i}} , as the macroscopic 'electric charge', makes e the macroscopic 'electric charge' for an electron, and enables the formula to be put into the familiar form of the coulomb potential:
V ( r ) = − 1 4 π ε 0 q 1 q 2 r {\displaystyle V(\mathbf {r} )={\frac {-1}{4\pi \varepsilon _{0}}}{\frac {q_{1}q_{2}}{r}}}
The force ( d V ( r ) d r {\displaystyle {\frac {dV(\mathbf {r} )}{dr}}} ) is therefore :
F ( r ) = 1 4 π ε 0 q 1 q 2 r 2 {\displaystyle F(\mathbf {r} )={\frac {1}{4\pi \varepsilon _{0}}}{\frac {q_{1}q_{2}}{r^{2}}}}
The derivation makes clear that the force law is only an approximation — it ignores the momentum of the input and output fermion lines, and ignores all quantum corrections (ie. the myriad possible diagrams with internal loops).
The Coulomb potential, and its derivation, can be seen as a special case of the Yukawa potential (specifically, the case where the exchanged boson - the photon - has no rest mass).
Scalar form[edit]
The absolute value of the force F between two point charges q and Q relates to the distance between the point charges and to the simple product of their charges. The diagram shows that like charges repel each other, and opposite charges mutually attract.
When it is of interest to know the magnitude of the electrostatic force (and not its direction), it may be easiest to consider a scalar version of the law. The scalar form of Coulomb's Law relates the magnitude and sign of the electrostatic force F acting simultaneously on two point charges q1 and q2 as follows:
| F | = k e | q 1 q 2 | r 2 {\displaystyle |{\boldsymbol {F}}|=k_{e}{|q_{1}q_{2}| \over r^{2}}}
where r is the separation distance and ke is Coulomb's constant. If the product q1q2 is positive, the force between the two charges is repulsive; if the product is negative, the force between them is attractive.[14]
Vector form[edit]
In the image, the vector F1 is the force experienced by q1, and the vector F2 is the force experienced by q2. When q1q2 > 0 the forces are repulsive (as in the image) and when q1q2 < 0 the forces are attractive (opposite to the image). The magnitude of the forces will always be equal.
Coulomb's law states that the electrostatic force F1 experienced by a charge, q1 at position r1, in the vicinity of another charge, q2 at position r2, in a vacuum is equal to:
F 1 = q 1 q 2 4 π ε 0 ( r 1 − r 2 ) | r 1 − r 2 | 3 = q 1 q 2 4 π ε 0 r ^ 21 | r 21 | 2 , {\displaystyle {\boldsymbol {F_{1}}}={q_{1}q_{2} \over 4\pi \varepsilon _{0}}{({\boldsymbol {r_{1}-r_{2}}}) \over |{\boldsymbol {r_{1}-r_{2}}}|^{3}}={q_{1}q_{2} \over 4\pi \varepsilon _{0}}{{\boldsymbol {{\hat {r}}_{21}}} \over |{\boldsymbol {r_{21}}}|^{2}},}
where r21 = r1 − r2, the unit vector r̂21 = r21/|r21|, and ε0 is the electric constant.
The vector form of Coulomb's law is simply the scalar definition of the law with the direction given by the unit vector, r̂21, parallel with the line from charge q2 to charge q1.[15] If both charges have the same sign (like charges) then the product q1q2 is positive and the direction of the force on q1 is given by r̂21; the charges repel each other. If the charges have opposite signs then the product q1q2 is negative and the direction of the force on q1 is given by −r̂21 = r̂12; the charges attract each other.
The electrostatic force F2 experienced by q2, according to Newton's third law, is F2 = −F1.
System of discrete charges[edit]
The law of superposition allows Coulomb's law to be extended to include any number of point charges. The force acting on a point charge due to a system of point charges is simply the vector addition of the individual forces acting alone on that point charge due to each one of the charges. The resulting force vector is parallel to the electric field vector at that point, with that point charge removed.
The force F on a small charge q at position r, due to a system of N discrete charges in vacuum is:
F ( r ) = q 4 π ε 0 ∑ i = 1 N q i r − r i | r − r i | 3 = q 4 π ε 0 ∑ i = 1 N q i R i ^ | R i | 2 , {\displaystyle {\boldsymbol {F(r)}}={q \over 4\pi \varepsilon _{0}}\sum _{i=1}^{N}q_{i}{{\boldsymbol {r-r_{i}}} \over |{\boldsymbol {r-r_{i}}}|^{3}}={q \over 4\pi \varepsilon _{0}}\sum _{i=1}^{N}q_{i}{{\boldsymbol {\widehat {R_{i}}}} \over |{\boldsymbol {R_{i}}}|^{2}},}
where qi and ri are the magnitude and position respectively of the ith charge, R̂i is a unit vector in the direction of Ri = r − ri (a vector pointing from charges qi to q).[15]
Continuous charge distribution[edit]
In this case, the principle of linear superposition is also used. For a continuous charge distribution, an integral over the region containing the charge is equivalent to an infinite summation, treating each infinitesimal element of space as a point charge dq. The distribution of charge is usually linear, surface or volumetric.
For a linear charge distribution (a good approximation for charge in a wire) where λ(r′) gives the charge per unit length at position r′, and dl′ is an infinitesimal element of length,
d q = λ ( r ′ ) d l ′ {\displaystyle dq=\lambda ({\boldsymbol {r'}})dl'} .[16]
For a surface charge distribution (a good approximation for charge on a plate in a parallel plate capacitor) where σ(r′) gives the charge per unit area at position r′, and dA′ is an infinitesimal element of area,
d q = σ ( r ′ ) d A ′ . {\displaystyle dq=\sigma ({\boldsymbol {r'}})\,dA'.}
For a volume charge distribution (such as charge within a bulk metal) where ρ(r′) gives the charge per unit volume at position r′, and dV′ is an infinitesimal element of volume,
d q = ρ ( r ′ ) d V ′ . {\displaystyle dq=\rho ({\boldsymbol {r'}})\,dV'.} [15]
The force on a small test charge q′ at position r in vacuum is given by the integral over the distribution of charge:
F = q ′ 4 π ε 0 ∫ d q r − r ′ | r − r ′ | 3 . {\displaystyle {\boldsymbol {F}}={q' \over 4\pi \varepsilon _{0}}\int dq{{\boldsymbol {r}}-{\boldsymbol {r'}} \over |{\boldsymbol {r}}-{\boldsymbol {r'}}|^{3}}.}
Simple experiment to verify Coulomb's law[edit]
Experiment to verify Coulomb's law.
It is possible to verify Coulomb's law with a simple experiment. Consider two small spheres of mass m and same-sign charge q, hanging from two ropes of negligible mass of length l. The forces acting on each sphere are three: the weight mg, the rope tension T and the electric force F.
In the equilibrium state:
T sin  θ 1 = F 1 {\displaystyle T\ \sin \theta _{1}=F_{1}\,\!}
(1)
and:
T cos  θ 1 = m g {\displaystyle T\ \cos \theta _{1}=mg\,\!}
(2)
Dividing (1) by (2):
sin  θ 1 cos  θ 1 = F 1 m g ⇒ F 1 = m g tan  θ 1 {\displaystyle {\frac {\sin \theta _{1}}{\cos \theta _{1}}}={\frac {F_{1}}{mg}}\Rightarrow F_{1}=mg\tan \theta _{1}}
(3)
Let L1 be the distance between the charged spheres; the repulsion force between them F1, assuming Coulomb's law is correct, is equal to
F 1 = q 2 4 π ϵ 0 L 1 2 {\displaystyle F_{1}={\frac {q^{2}}{4\pi \epsilon _{0}L_{1}^{2}}}}
(Coulomb's law)
so:
q 2 4 π ϵ 0 L 1 2 = m g tan  θ 1 {\displaystyle {\frac {q^{2}}{4\pi \epsilon _{0}L_{1}^{2}}}=mg\tan \theta _{1}\,\!}
(4)
If we now discharge one of the spheres, and we put it in contact with the charged sphere, each one of them acquires a charge q/2. In the equilibrium state, the distance between the charges will be L2 < L1 and the repulsion force between them will be:
F 2 = ( q 2 ) 2 4 π ϵ 0 L 2 2 = q 2 4 4 π ϵ 0 L 2 2 {\displaystyle F_{2}={\frac {{({\frac {q}{2}})}^{2}}{4\pi \epsilon _{0}L_{2}^{2}}}={\frac {\frac {q^{2}}{4}}{4\pi \epsilon _{0}L_{2}^{2}}}\,\!}
(5)
We know that F2 = mg tan θ2. And:
q 2 4 4 π ϵ 0 L 2 2 = m g tan  θ 2 {\displaystyle {\frac {\frac {q^{2}}{4}}{4\pi \epsilon _{0}L_{2}^{2}}}=mg\tan \theta _{2}}
Dividing (4) by (5), we get:
( q 2 4 π ϵ 0 L 1 2 ) ( q 2 4 4 π ϵ 0 L 2 2 ) = m g tan  θ 1 m g tan  θ 2 ⇒ 4 ( L 2 L 1 ) 2 = tan  θ 1 tan  θ 2 {\displaystyle {\frac {\left({\cfrac {q^{2}}{4\pi \epsilon _{0}L_{1}^{2}}}\right)}{\left({\cfrac {\frac {q^{2}}{4}}{4\pi \epsilon _{0}L_{2}^{2}}}\right)}}={\frac {mg\tan \theta _{1}}{mg\tan \theta _{2}}}\Rightarrow 4{\left({\frac {L_{2}}{L_{1}}}\right)}^{2}={\frac {\tan \theta _{1}}{\tan \theta _{2}}}}
(6)
Measuring the angles θ1 and θ2 and the distance between the charges L1 and L2 is sufficient to verify that the equality is true taking into account the experimental error. In practice, angles can be difficult to measure, so if the length of the ropes is sufficiently great, the angles will be small enough to make the following approximation:
tan  θ ≈ sin  θ = L 2 l = L 2 l ⇒ tan  θ 1 tan  θ 2 ≈ L 1 2 l L 2 2 l {\displaystyle \tan \theta \approx \sin \theta ={\frac {\frac {L}{2}}{l}}={\frac {L}{2l}}\Rightarrow {\frac {\tan \theta _{1}}{\tan \theta _{2}}}\approx {\frac {\frac {L_{1}}{2l}}{\frac {L_{2}}{2l}}}}
(7)
Using this approximation, the relationship (6) becomes the much simpler expression:
L 1 2 l L 2 2 l ≈ 4 ( L 2 L 1 ) 2 ⇒ {\displaystyle {\frac {\frac {L_{1}}{2l}}{\frac {L_{2}}{2l}}}\approx 4{\left({\frac {L_{2}}{L_{1}}}\right)}^{2}\Rightarrow \,\!} L 1 L 2 ≈ 4 ( L 2 L 1 ) 2 ⇒ L 1 L 2 ≈ 4 3 {\displaystyle {\frac {L_{1}}{L_{2}}}\approx 4{\left({\frac {L_{2}}{L_{1}}}\right)}^{2}\Rightarrow {\frac {L_{1}}{L_{2}}}\approx {\sqrt[{3}]{4}}\,\!}
(8)
In this way, the verification is limited to measuring the distance between the charges and check that the division approximates the theoretical value.
Atomic forces[edit]
See also: Coulomb explosion
Coulomb's law holds even within atoms, correctly describing the force between the positively charged atomic nucleus and each of the negatively charged electrons. This simple law also correctly accounts for the forces that bind atoms together to form molecules and for the forces that bind atoms and molecules together to form solids and liquids. Generally, as the distance between ions increases, the force of attraction, and binding energy, approach zero and ionic bonding is less favorable. As the magnitude of opposing charges increases, energy increases and ionic bonding is more favorable.
See also[edit]
Wikimedia Commons has media related to Coulomb force.
Electronics portal
Biot–Savart law
Darwin Lagrangian
Electromagnetic force
Gauss's law
Method of image charges
Molecular modelling
Newton's law of universal gravitation, which uses a similar structure, but for mass instead of charge
Static forces and virtual-particle exchange
Notes[edit]
^ Jump up to: a b Stewart, Joseph (2001). Intermediate Electromagnetic Theory. World Scientific. p. 50. ISBN 981-02-4471-1
Jump up ^ Simpson, Brian (2003). Electrical Stimulation and the Relief of Pain. Elsevier Health Sciences. pp. 6–7. ISBN 0-444-51258-6
Jump up ^ Baigrie, Brian (2007). Electricity and Magnetism: A Historical Perspective. Greenwood Press. pp. 7–8. ISBN 0-313-33358-0
Jump up ^ Chalmers, Gordon (1937). "The Lodestone and the Understanding of Matter in Seventeenth Century England". Philosophy of Science. 4 (1): 75–95. doi:10.1086/286445
Jump up ^ Socin, Abel (1760). Acta Helvetica Physico-Mathematico-Anatomico-Botanico-Medica (in Latin). 4. Basileae. pp. 224–25.
Jump up ^ Heilbron, J.L. (1979). Electricity in the 17th and 18th Centuries: A Study of Early Modern Physics. Los Angeles, California: University of California Press. pp. 460–462 and 464 (including footnote 44). ISBN 0486406881.
Jump up ^ Schofield, Robert E. (1997). The Enlightenment of Joseph Priestley: A Study of his Life and Work from 1733 to 1773. University Park: Pennsylvania State University Press. pp. 144–56. ISBN 0-271-01662-0.
Jump up ^ Priestley, Joseph (1767). The History and Present State of Electricity, with Original Experiments. London, England. p. 732.
May we not infer from this experiment, that the attraction of electricity is subject to the same laws with that of gravitation, and is therefore according to the squares of the distances; since it is easily demonstrated, that were the earth in the form of a shell, a body in the inside of it would not be attracted to one side more than another?
Jump up ^ Elliott, Robert S. (1999). Electromagnetics: History, Theory, and Applications. ISBN 978-0-7803-5384-8.
Jump up ^ Robison, John (1822). Murray, John, ed. A System of Mechanical Philosophy. 4. London, England.
On page 68, the author states that in 1769 he announced his findings regarding the force between spheres of like charge. On page 73, the author states the force between spheres of like charge varies as x−2.06:
The result of the whole was, that the mutual repulsion of two spheres, electrified positively or negatively, was very nearly in the inverse proportion of the squares of the distances of their centres, or rather in a proportion somewhat greater, approaching to x−2.06.
When making experiments with charged spheres of opposite charge the results were similar, as stated on page 73:
When the experiments were repeated with balls having opposite electricities, and which therefore attracted each other, the results were not altogether so regular and a few irregularities amounted to 1⁄6 of the whole; but these anomalies were as often on one side of the medium as on the other. This series of experiments gave a result which deviated as little as the former (or rather less) from the inverse duplicate ratio of the distances; but the deviation was in defect as the other was in excess.
Nonetheless, on page 74 the author infers that the actual action is related exactly to the inverse duplicate of the distance:
We therefore think that it may be concluded, that the action between two spheres is exactly in the inverse duplicate ratio of the distance of their centres, and that this difference between the observed attractions and repulsions is owing to some unperceived cause in the form of the experiment.
On page 75, the authour compares the electric and gravitational forces:
Therefore we may conclude, that the law of electric attraction and repulsion is similar to that of gravitation, and that each of those forces diminishes in the same proportion that the square of the distance between the particles increases.
Jump up ^ Maxwell, James Clerk, ed. (1967) [1879]. "Experiments on Electricity: Experimental determination of the law of electric force.". The Electrical Researches of the Honourable Henry Cavendish... (1st ed.). Cambridge, England: Cambridge University Press. pp. 104–113.
On pages 111 and 112 the author states:
We may therefore conclude that the electric attraction and repulsion must be inversely as some power of the distance between that of the 2 + 1⁄50 th and that of the 2 − 1⁄50 th, and there is no reason to think that it differs at all from the inverse duplicate ratio.
^ Jump up to: a b Coulomb (1785a) "Premier mémoire sur l’électricité et le magnétisme," Histoire de l’Académie Royale des Sciences, pages 569-577 — Coulomb studied the repulsive force between bodies having electrical charges of the same sign:
Il résulte donc de ces trois essais, que l'action répulsive que les deux balles électrifées de la même nature d'électricité exercent l'une sur l'autre, suit la raison inverse du carré des distances.
Translation: It follows therefore from these three tests, that the repulsive force that the two balls — [that were] electrified with the same kind of electricity — exert on each other, follows the inverse proportion of the square of the distance.
Coulomb also showed that oppositely charged bodies obey an inverse-square law of attraction.
Jump up ^ Jackson, J. D. (1998) [1962]. Classical Electrodynamics (3rd ed.). New York: John Wiley & Sons. ISBN 978-0-471-30932-1. OCLC 535998.
Jump up ^ Coulomb's law, Hyperphysics
^ Jump up to: a b c Coulomb's law, University of Texas
Jump up ^ Charged rods, PhysicsLab.org
ke = H/m is not correct it must be F/m
References[edit]
Coulomb, Charles Augustin (1788) [1785]. "Premier mémoire sur l'électricité et le magnétisme". Histoire de l’Académie Royale des Sciences. Imprimerie Royale. pp. 569–577.
Coulomb, Charles Augustin (1788) [1785]. "Second mémoire sur l'électricité et le magnétisme". Histoire de l’Académie Royale des Sciences. Imprimerie Royale. pp. 578–611.
Griffiths, David J. (1998). Introduction to Electrodynamics (3rd ed.). Prentice Hall. ISBN 0-13-805326-X.
Tipler, Paul A.; Mosca, Gene (2008). Physics for Scientists and Engineers (6th ed.). New York: W. H. Freeman and Company. ISBN 0-7167-8964-7. LCCN 2007010418.
Young, Hugh D.; Freedman, Roger A. (2010). Sears and Zemansky's University Physics : With Modern Physics (13th ed.). Addison-Wesley (Pearson). ISBN 978-0-321-69686-1.
External links[edit]
Coulomb's Law on Project PHYSNET
Electricity and the Atom—a chapter from an online textbook
A maze game for teaching Coulomb's Law—a game created by the Molecular Workbench software
Electric Charges, Polarization, Electric Force, Coulomb's Law Walter Lewin, 8.02 Electricity and Magnetism, Spring 2002: Lecture 1 (video). MIT OpenCourseWare. License: Creative Commons Attribution-Noncommercial-Share Alike.
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Siri (given name)
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This article is about the Scandinavian female given name derived from "Sigrid". For other uses, see Siri (disambiguation).
Siri
Gender
Female
Origin
Meaning
Beautiful victory
Other names
Related names
Sigrid
Siri is a Scandinavian female given name. It is a short form of Sigrid, of Old Norse origin, and literally meaning "beautiful victory", from Old Norse sigr (victory) and Old Norse fríðr (beautiful). The name Siri has been widely used since the Middle Ages, and is a common name in Norway, Sweden and the Faroe Islands. It was common in Norway until the 18th century, when its usage declined, but saw new high popularity in the 20th century. In Sweden the name gained new popularity around 1900, and has again become increasingly popular in the last years. The Faroese spelling of the name is Sirið;[1] the ð is not pronounced. The other spelling without ð is also common.[2] To a lesser extent it is also used in Denmark.
People[edit]
Siri Bjerke, Norwegian cabinet minister
Siri Broch Johansen, Norwegian author
Siri Dokken, Norwegian artist
Siri von Essen, Swedish actress and wife of August Strindberg.
Siri Hustvedt, American author
Siri Lindley, American triathlete and coach
Siri Nilsen (born 1985), Norwegian singer, songwriter, musician, and voice actress
Sirið Stenberg, Faroese politician, member of the Løgting since 2011
References[edit]
Jump up ^ Fmn.fo (chose "Konufólkanøvn" and the letter S)
Jump up ^ Hagstova.fo, chose the section "Fólkanøvn" and "Konufólkanøvn (2001-2012)"
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Pepper Potts
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Pepper Potts
Pepper Potts in Superior Iron Man #6 (May 2015)
Art by Laura Braga
Publication information
Publisher
Marvel Comics
First appearance
As Pepper Potts:
Tales of Suspense #45 (September 1963)

As Rescue:
The Invincible Iron Man #10 (May 2009)
Created by
Pepper Potts:
Stan Lee
Robert Bernstein
Don Heck

Rescue:
Matt Fraction
Salvador Larroca
In-story information
Full name
Virginia "Pepper" Potts
Team affiliations
The Order
The Initiative
Stark Industries
Supporting character of
Iron Man
Notable aliases
Hera, Rescue, Coast Guard, Iron Man, Iron Woman
Virginia "Pepper" Potts is a fictional supporting character appearing in books published by Marvel Comics, particularly those featuring Iron Man, in which she serves as a romantic love interest of Tony Stark. Created by writers Stan Lee and Robert Bernstein and artist Don Heck, she first appeared in Tales of Suspense #45 (Sept. 1963). In 2007, she joined the Fifty State Initiative under the codename Hera. In 2009, she assumes the identity of Rescue after being given her own suit of a variation of Iron Man armor by Tony Stark.[1][2][3]
The character is portrayed by Gwyneth Paltrow in the Marvel Cinematic Universe films Iron Man, Iron Man 2, The Avengers, Iron Man 3, Spider-Man: Homecoming, Avengers: Infinity War and its untitled sequel.
Contents
1 Publication history
2 Fictional character biography
2.1 Early history
2.2 The Order
2.3 2008 – present
3 Powers and abilities
4 Other versions
5 In other media
5.1 Television
5.2 Film
5.3 Animation
5.4 Video games
5.5 Theatre
6 References
7 External links
Publication history[edit]
Virginia "Pepper" Potts first appeared in Tales of Suspense #45 (September 1963), which was written by Robert Bernstein with a story plot by Stan Lee and illustrated by Don Heck. Though she was named Pepper Potts from the start, Stark addresses her as "Kitty" in one panel, which is thought to be a typo. Heck modeled Potts as Ann B. Davis’ character of Schultzy from The Bob Cummings Show, and she is rendered with brown hair done up in a hairdo similar to Schultzy's. Someone on the creative team or in editorial came to feel that the resemblance was too great, and in Tales of Suspense #50, Potts' look was altered to give her red hair and a different hairdo.
Fictional character biography[edit]
Early history[edit]
Potts is originally a member of a secretarial pool, and gets her job by fixing an accounting error made by Stark. She is depicted initially as being infatuated with Stark, and rejects the advances of Stark's chauffeur and assistant Happy Hogan, who debuted in the same issue, with acerbic remarks. As Stark's affection for her grows in the ensuing issues, she becomes part of a love triangle between the two men, and eventually falls in love with and marries Hogan, eloping with him in Tales of Suspense #91.[4]
Pepper and Happy Hogan.
Pepper and Happy eventually leave Stark Industries, settling in the Rocky Mountains and then finally in Cleveland, where they adopt children after being unable to conceive, and disappear from the main Iron Man storyline. After being kidnapped by Stark's rival Obadiah Stane, Pepper tells Tony to stay out of their lives. Pepper and Happy soon divorce after she has an affair with a former college boyfriend. After Tony Stark's return from the Heroes Reborn universe, Pepper and Happy join Tony at his new company, Stark Solutions, and once again become core characters. After some time, Happy and Pepper once again became involved and remarry, eventually considering conceiving a child to supplement their adopted children. Stark entrusts Pepper with a special remote that could shut him down. However, Pepper, tortured by the responsibility, is forced to return it, and the trauma causes her to miscarry. Stark is able to deal with the remote, but feels guilty that he has placed her in such danger.
After Happy sustains massive injuries in a fight with Spymaster during the 2006-2007 "Civil War" storyline, Pepper requests that Tony turn off Happy's life support. Happy dies in Invincible Iron Man (vol. 4) #14.
The Order[edit]
After the events of the "Civil War" story line, Pepper joins the Fifty State Initiative as a member of The Order, a government sanctioned superhero team operating within California. She assumes the moniker of the Greek goddess Hera, and uses advanced computer-hardware and prosthetics to monitor and coordinate the team's missions. Upon the absorption of The Order into the Initiative, Tony Stark offers her a job on the special-projects team at Stark Enterprises, which she accepts.[volume & issue needed]
2008 – present[edit]
Pepper Potts resumes her activities as personal secretary of Tony Stark. When Pepper is caught in a terrorist explosion caused by Ezekiel "Zeke" Stane, she sustains multiple internal injuries, including shrapnel wounds, and rendered unable to withstand a prolonged surgery. In response, Tony embeds a strong magnet (similar in appearance to the arc reactor of the movie) in her chest, essentially turning Pepper into a cyborg dependent on keeping her chest magnet engaged to stay alive, as he was once.[5]
Pepper's body is further enhanced with new cybernetics and upgrades to the magnet, which are based on Danny Rand's battery designs, and which afford Pepper new super abilities.[6]
When Tony is blamed for the Skrull invasion of Earth that occurs in the 2008 storyline "Secret Invasion", S.H.I.E.L.D. is taken over by Norman Osborn, replaced with H.A.M.M.E.R., and Stark and Maria Hill are fired, along with all of S.H.I.E.L.D.'s employees. Tony realizes that Osborn is after the identities of superhumans that registered with the government following the passage of the Superhuman Registration Act that occurred during the "Civil War" storyline, which is stored in a database in his brain. Stark decides to go underground with Hill, and to wipe the knowledge in his own brain. Stark makes Pepper the new CEO of Stark Industries, trusting only her to shut down the company in his absence. Pepper discovers a secret room in Stark's office which contains a suit of armor that he made especially for her,[1] which she uses under the name Rescue.[2] Though Osborn has seized all Stark Industries facilities and equipment, Pepper states that all components of her armor are legal and that the design specifications are available to anyone. Despite Osborn threatening her loved ones with prison if she interferes with his search for Tony or attempts any more heroic actions, after being freed she endeavors to find Tony herself.[7] They are reunited in Russia,[8] and consummate a now-sexual relationship, but are subsequently captured and tortured by Madame Masque, who was assigned by Norman Osborn to track Stark down. Stark admits that he had loved Masque in the past,[9] but when pressed to make a choice, with his own life on the line, Tony chooses Pepper. Pepper decides to engage Masque in a physical altercation in order to provide a distraction for Stark to escape.[10]
During the 2009 "World's Most Wanted Storyline" (which ran concurrently with Marvel's company-wide storyline "Dark Reign"), Pepper, after defeating Masque, disguises herself as the former, infiltrating H.A.M.M.E.R. while presenting the Rescue armor to Osborn as spoils of battle. Pepper reveals herself when she rescues Black Widow and Maria Hill from Osborn's imprisonment, while the Rescue suit uploads a virus into H.A.M.M.E.R.'s computers, taking control of the Helicarrier's armory of suits.[11] They then retrieve the hard drive that Hill was assigned by Stark to get, escaping to give it to Captain America in order to restore Starks' mind.[12] As part of "re-booting" Tony (in a vegetative state), the magnet in her chest is removed and placed into his.[13]
Though Stark's memories are restored from a somewhat years-old backup, he no longer remembers the events of the "Civil War" nor his role in it, its aftermath or his affair with Pepper. Pepper survives the removal of her chest magnet, but demands that a new one similar to Tony's own chest repulsor be re-installed, which is done. Recovered, Stark also gifts Pepper with a new Rescue armor, complete with JARVIS.[14]
During the 2011 "Stark Resilient" storyline, when Justine Hammer and Sasha Hammer use their own armored enforcer Detroit Steel to attempt to sabotage Stark Resilient (Tony's new company) and its design for a repulsor technology-powered vehicle, Pepper joins War Machine in helping Stark, during which Pepper experiences a near-death experience in which JARVIS, masquerading as Happy, gives Pepper a cryptic warning of the future.[15]
In the 2012 storyline "The Future", Pepper returns to her civilian life following her destruction of J.A.R.V.I.S., the artificial intelligence that helped her control her Rescue armor,[3] after its compromise led it to go rogue and attempt to kidnap her.[16] She became engaged to Marc Kumar, a public relations and marketing consultant, but broke off the relationship after he briefly became a supervillain.[citation needed]
After Tony undergoes a moral inversion following a confrontation with the psychic Red Skull, Pepper attempts to oppose his efforts to release Extremis on a large scale[17] with the aid of an A.I. back-up of Tony's mind he created eight years ago in the event of his mind being attacked in such a manner.[18] Although the A.I. concludes that Tony's mind is irreversibly twisted, and is subsequently destroyed by Tony, Pepper states that she bought one of the largest media companies from under him which she will use to destroy his reputation by broadcasting his plans to the rest of the world. She then proclaims that any attempts he makes to create his 'perfect world' will have to be carried out with people fully aware that he is now nothing but a monster.[19]
As part of the "All-New, All-Different Marvel" brand, Pepper Potts has not been seen in the public life. When Tony Stark (who was no longer inverted) had hired Mary Jane Watson to work for Stark Industries, Peter Parker attempted to recruit Pepper to work for Parker Industries. Pepper declined the offer.[20]
Appearing in her Rescue armor following the "Civil War II" storyline, Pepper Potts confronted Riri Williams and her Tony Stark A.I. in an attempt to tell Riri the problems of being a superhero only for them to be attacked by Techno Golem and her Biohack Ninjas.[21] As Riri flee, Pepper fights against Techno Golem and her Biohack Ninjas as Techno Golem tries to get answers from Pepper on how she knows Riri.[22] When Techo Golem's armor breaks and Tomoe tries to attack Riri, Pepper fires her Rescue armor's gauntlets at Tomoe which knocked her out. Upon Sharon Carter formally meeting Riri upon the arrest of Tomoe and the Biohack Ninjas, Pepper states to Riri that they will talk again as she flies off in her Rescue armor.[23] Pepper Potts was present with Mary Jane Watson, Friday, the Tony Stark A.I., and Tony Stark's biological mother Amanda Armstrong when they are in the Hall of Armor where Riri voices her knowledge of each of the Iron Man armors. When Amanda Armstrong offers to have Riri let Tony Stark's labs be her base of operations, Riri is hesitant as Pepper encourages her.[24]
During the "Secret Empire" storyline, Rescue is among the superheroes that are part of the Underground where she is part of their resistance against Hydra following their takeover of the United States.[25]
Powers and abilities[edit]
The Stark-tech mag-field generator implanted in Pepper’s chest was not weapons-based like Stark's, but borrowed non-weaponized electromagnetic technology from Rand Industries, which caused a number of physical changes to her body. It cured her tinnitus, improving her hearing. It allows her to sense electromagnetic fields, and manipulate them to levitate her body.[6]
Potts' Stark-tech armor suit,[1] which is designated Mark 1616,[26] but named Rescue by Potts,[2] represents a hybrid of repulsor technology and portable electromagnetic super-field generators that give the suit flight, speed, strength, and magnetic-field manipulation. Its electromagnetic force fields are powerful enough to enable Rescue to stop a falling jet airliner without physical contact with it,[27] and can also be used as an offensive weapon with other armored opponents.[2] The suit's physical strength enables it to hold up a stilt mansion felled by an earthquake,[27] and to rip the lower leg of the Black armor.[16] The armor also features an artificial intelligence named J.A.R.V.I.S. that acts as a guide for Potts.[26] During the 2012 storyline "The Future", Potts and Carson Wyche come to suspect that J.A.R.V.I.S. has been compromised, and when they attempt to troubleshoot the Rescue helmet, J.A.R.V.I.S. takes control of the Rescue armor, and takes Potts and Wyche hostage.[16] J.A.R.V.I.S. is disabled by James Rhodes with a source-focused electromagnetic pulse from the Black armor,[28] and is eventually destroyed by Potts, ending her career as Rescue.[3] She has a new Rescue armor in the subsequent series Superior Iron Man, armed with sonic disruptors.[29]
Other versions[edit]
In the Amalgam Comics Universe, DC Comics' Green Lantern and Marvel's Iron Man are combined to create Iron Lantern.[30] Iron Lantern is secretly Hal Stark, owner of Stark Aircraft, a developer of experimental aircraft. One of his test pilots is Pepper Ferris (an amalgamation of Pepper Potts and DC's Carol Ferris). Like both her DC and Marvel counterparts, she is involved in a love triangle, this time with Stark and his chief mechanic Happy Kalmaku (an amalgamation of Marvel's Happy Hogan and DC's Thomas Kalmaku). When Pepper comes in contact with a mysterious alien gem, she is transformed into Madame Sapphire (a combination of Marvel's Madame Masque and DC's Star Sapphire). Pepper Ferris first appeared in Iron Lantern #1 (April 1997), published jointly by Marvel and DC.
In the alternate universe of the "Heroes Reborn" storyline, she and Iron Man are lovers, although she can also be seen in a relationship with Happy Hogan. Stark is forced to leave her unexpectedly and without explanation, as his very presence in the universe will endanger her life and the lives of everyone else.[volume & issue needed]
She appears in the Marvel Zombies universe in Marvel Zombies Return, having just submitted her resignation to Stark, who at this point is a near-useless drunk. However, when the zombie Giant Man initiates an outbreak at Stark International, Pepper and Happy are among the zombified casualties. She is killed by Stark when he vomits a nanite-ridden formula upon her, which dissolves Pepper into a skeleton.[31]
The Ultimate Marvel version of the character can be seen during Ultimates 2. She and Happy (with whom she appears to be in a relationship) can be seen monitoring Tony when he uses the armor.[32]
In The Invincible Iron Man #500, in a flashforward to an apocalyptic future 41 years ahead where the Mandarin has conquered the world, an aged version of Tony defeats his long-time foe with the help of his son Howard Anthony Stark and his granddaughter Ginny Stark, but Howard and Tony sacrifice themselves in the process. At the close of the story, Ginny buries the two next to a gravestone with the name Virginia Potts Stark. Howard is also said to be 41 years old, suggesting that he will be born within the following year.[33]
In other media[edit]
Television[edit]
Pepper Potts has appeared in the Invincible Iron Man segments of The Marvel Super Heroes, voiced by Peg Dixon.
Pepper Potts as seen in Iron Man: Armored Adventures.
Pepper Potts appears in Iron Man: Armored Adventures, voiced by Anna Cummer. This incarnation's full name is Patricia "Pepper" Potts. Like Tony Stark and Rhodey Rhodes, she is a teenager, and is initially unaware of Iron Man's secret identity, though she later learns it after he saves her life.[34] She eventually learns to use the Iron Man stealth armor,[35][36][37][38] and as in the comics, is given one of her own called Rescue.[39]
Pepper Potts appears in The Avengers: Earth's Mightiest Heroes voiced by Dawn Olivieri.[40]
Pepper Potts has a few cameos in Marvel Anime: Iron Man, voiced by Hiroe Oka in the Japanese version and by Cindy Robinson in the English dub.
Pepper Potts appears in the Lego Marvel Super Heroes: Maximum Overload mini-series, voiced by Grey DeLisle.
Pepper Potts appears in Marvel Disk Wars: The Avengers, voiced by Fumie Mizusawa in the Japanese version.
Film[edit]
Pepper Potts is mentioned in Ultimate Avengers 2.
Pepper Potts appeared in The Invincible Iron Man, voiced by Elisa Gabrielli with an apparent British accent.
Gwyneth Paltrow as Pepper Potts in the 2008 film Iron Man.
Gwyneth Paltrow portrays the character in the Marvel Cinematic Universe:[41][42]
In Iron Man, Tony Stark notes that Potts, his secretary/personal aide, is virtually the only trustworthy individual Stark has at the company.
In Iron Man 2, Pepper is promoted to CEO of Stark Industries by Tony Stark. She later attempts to resign following Ivan Vanko's attack on the Stark Expo, but Stark does not accept it.[43] At the end of the film, Pepper becomes Tony's girlfriend.
In The Avengers, Potts is instrumental in helping with the development of Stark Tower and Tony's assistance to S.H.I.E.L.D. She also has developed a friendship with Phil Coulson.
In Iron Man 3, Pepper is still the CEO of Stark Industries and has moved in with Tony. During an attack on Stark's mansion, Tony wills the Mark 42 armor to encase her thus saving her and Maya Hansen, whom Potts rescues using the armor. After being captured, Aldrich Killian uses her as a test subject for the Extremis process and thus as leverage to force Tony to complete the work to make Extremis stable. However, she turns the tables on Killian by using her own Extremis powers to kill him. Tony is able to modify Extremis so that it is no longer a danger to herself or others.
Pepper does not appear in Avengers: Age of Ultron, but is mentioned along with Jane Foster during a conversation involving Maria Hill (asking why they're not at the party), Thor and Stark. Pepper is mentioned to still be the CEO of Stark Industries by Tony. Any doubts about her romance with Tony are put to rest at the end of the film, after Stark mentions wanting to settle down in a peaceful, quiet place with her (having been inspired by Clint Barton's family life).
Pepper is mentioned again in Captain America: Civil War. It is revealed that she and Tony are "taking a break". Stark explains to Steve Rogers that the strain of being Iron Man finally took its toll on their relationship, and believes the Sokovia Accords would be a blessing, since it's strongly implied Pepper would consider Tony more responsible if Iron Man were acting in less of a vigilante role.
Pepper Potts appears at the end of Spider-Man: Homecoming. It is revealed that she and Tony have rekindled their relationship, with Tony planning to propose to her in a press conference.
Potts appears in the beginning of Avengers: Infinity War, where Tony persuades her to have a child with him. They plan to have dinner later that day, but the arrival of the Children of Thanos forces Tony to abandon the plan. She later calls Tony, begging him to get off of Ebony Maw's spaceship, before the call breaks off due to weak signal.
Paltrow will reprise the role in the untitled Avengers film, slated for release in 2019.[44]
Animation[edit]
Pepper Potts appears in Iron Man: Rise of Technovore, voiced by Hiroe Oka in the Japanese version and by Kate Higgins in the English dub.[citation needed] In the film, she's taking vacation time on an island mansion Tony Stark gave her as a gift for a past blunder. However, she's forced back to work when Iron Man begins investigating the mysterious technology that ruined the launch of his satellite and wounded War Machine.
Video games[edit]
Pepper Potts is mentioned numerous times in Marvel: Ultimate Alliance. Edwin Jarvis asks the player to fetch a pair of cufflinks which Pepper gifted to Tony Stark.
Pepper Potts appears in the 2008 video game Iron Man and the 2010 game Iron Man 2, voiced by Meredith Monroe. These games are based on the films of the same name.
Pepper Potts appears in the Marvel Pinball video game, voiced by Tara Platt.
Rescue makes a cameo appearance in Strider Hiryu's ending in Ultimate Marvel vs. Capcom 3. She is seen fighting against the Reavers.
Rescue is a playable character in Marvel Super Hero Squad Online, voiced by Laura Bailey.
Rescue appears as an unlockable character in Marvel: Avengers Alliance.
Pepper Potts appears as a non-playable character in Marvel Heroes, voiced by Brett Pels.
Pepper Pott and her Rescue form appear in Lego Marvel Super Heroes, voiced again by Laura Bailey. Both Pepper Potts and Rescue appear as playable characters
Pepper Potts appear in Lego Marvel's Avengers where Gwyneth Paltrow's archive recordings were used. Her Rescue form also appears.
Pepper Potts appear in Marvel Avengers Academy. She is initially as Nick Fury's assistant. On March 20, 2016, Pepper Potts' Rescue form is obtainable through limited time.
Theatre[edit]
Pepper Potts will appear in the Marvel Universe: LIVE! stage show.[45]
References[edit]
^ Jump up to: a b c Fraction, Matt (w), Larocca, Salvador (a). "World's Most Wanted Part 3: No Future" The Invincible Iron Man v5, 11 (April 2009), Marvel Comics
^ Jump up to: a b c d Fraction, Matt (w), Larocca, Salvador (a). "World's Most Wanted Part 7: The Shape of the World These Days" The Invincible Iron Man 14 (August 2009), Marvel Comics
^ Jump up to: a b c Fraction, Matt (w), Larocca, Salavdor (a). "The Future Part 6: Independence Day" The Invincible Iron Man 526 (Dec. 2012), Marvel Comics
Jump up ^ Cronin, Brian (June 29, 2010). "Foggy Ruins of Time – Which Brady Bunch Actress Was Pepper Potts Based On?". Comic Book Resources.
Jump up ^ Fraction, Matt (w), Larocca, Salvador (a). "The Five Nightmares Part 3: Pepper Potts At the End of the World" The Invincible Iron Man 3 (Sept. 2008), Marvel Comics
^ Jump up to: a b Fraction, Matt (w), Larocca, Salvador (a). "The Five Nightmares Part 4: Neutron Bomb Heart" The Invincible Iron Man 4 (October 2008), Marvel Comics
Jump up ^ Fraction, Matt (w), Larocca, Salvador (a). "World's Most Wanted Part 7: The Shape of the World These Days" The Invincible Iron Man v5, 14 (August 2009), Marvel Comics
Jump up ^ Fraction, Matt (w), Larocca, Salvador (a). "World's Most Wanted Part 6: Some King of the World" The Invincible Iron Man v5, 14 (July 2009), Marvel Comics
Jump up ^ Fraction, Matt (w), Larocca, Salvador (a). "World's Most Wanted Part 8: The Danger We're All In" The Invincible Iron Man v5, 15 (Sept. 2009), Marvel Comics
Jump up ^ Fraction, Matt (w), Larocca, Salvador (a). "World's Most Wanted Part 9: Titan of the Nuclear Age" The Invincible Iron Man v5, 16 (October 2009), Marvel Comics
Jump up ^ Fraction, Matt (w), Larocca, Salvador (a). "World's Most Wanted Part 11: Kids with Guns vs. The Eternal Angel of Death" The Invincible Iron Man v5, 18 (Nov. 2009), Marvel Comics
Jump up ^ Fraction, Matt (w), Larocca, Salvador (a). "World's Most Wanted Conclusion: Into the White (Einstein on the Beach)" The Invincible Iron Man v5, 19 (Dec. 2009), Marvel Comics
Jump up ^ Fraction, Matt (w), Larocca, Salvador (a). "Stark: Disassembled Part 2: Digging in the Dirt" The Invincible Iron Man v5, 21 (February 2010), Marvel Comics
Jump up ^ Matt Fraction (w), Salvador Larocca (a). "Stark Resilient Part 4: Grand Mal Tokyo Moron Party" The Invincible Iron Man v5, 28 (Sept. 2010), Marvel Comics
Jump up ^ Matt Fraction (w), Salvador Larocca (a). "Stark Resilient Part 8: Drones Scream Down" The Invincible Iron Man v5, 32 (January 2011), Marvel Comics
^ Jump up to: a b c Fraction, Matt (w), Larocca, Salavdor (a). "The Future Part 3: Swarm" The Invincible Iron Man 523 (October 2012), Marvel Comics
Jump up ^ Superior Iron Man #1
Jump up ^ Superior Iron Man #7
Jump up ^ Superior Iron Man #9
Jump up ^ Amazing Spider-Man Vol. 4 #12
Jump up ^ Invincible Iron Man Vol. 3 #3
Jump up ^ Invincible Iron Man Vol. 3 #4
Jump up ^ Invincible Iron Man Vol. 3 #5
Jump up ^ Invincible Iron Man Vol. 3 #6
Jump up ^ Secret Empire #1
^ Jump up to: a b Fraction, Matt (w), Larocca, Salvador (a). "World's Most Wanted Part 4: Breach" The Invincible Iron Man 11 (May 2009), Marvel Comics
^ Jump up to: a b Fraction, Matt (w), Larocca, Salvador (a). "World's Most Wanted Part 5: The High-End Technology of Ultramodern Destruction" The Invincible Iron Man 12 (April 2009), Marvel Comics
Jump up ^ Fraction, Matt (w), Larocca, Salavdor (a). "The Future Part 4: Armor War" The Invincible Iron Man 524 (Nov. 2012), Marvel Comics
Jump up ^ Superior Iron Man #9. Marvel Comics.
Jump up ^ Who's Who Handbook of the Amalgam Universe
Jump up ^ "Marvel Zombies Return" #2 (2009)
Jump up ^ Millar, Mark (w), Hitch, Bryan (a). Ultimates 2 #3 Marvel Comics.
Jump up ^ Fraction, Matt (w), Kano (a). "The New Iron Age" The Invincible Iron Man 500 (March 2011), Marvel Comics
Jump up ^ "Whiplash". Iron Man: Armored Adventures. Season 1. Episode 5. May 15, 2009. Nicktoons.
Jump up ^ "Hostile Takeover". Iron Man: Armored Adventures. Season 2. Episode 15. March 7, 2012. Nicktoons.
Jump up ^ "Doomsday". Iron Man: Armored Adventures. Season 2. Episode 20. June 13, 2012. Nicktoons.
Jump up ^ "The Invincible Iron Man Part 2: Reborn". Iron Man: Armored Adventures. Season 2. Episode 2. July 20, 2011. Nicktoons.
Jump up ^ "Heavy Mettle". Iron Man: Armored Adventures. Season 2. Episode 13. November 26, 2011. Nicktoons.
Jump up ^ "Dragonseed". Iron Man: Armored Adventures. Season 2. Episode 24. July 11, 2012. Nicktoons.
Jump up ^ Jenna Busch (2010-02-08). "AVENGERS Animated Assembling w/ Phil Lamarr". Newsarama. Retrieved 2010-02-08.
Jump up ^ Krupa, Daniel (May 9, 2011). "Gwyneth Paltrow Talks Avengers" Archived 2012-03-01 at the Wayback Machine.. IGN.
Jump up ^ Wales, George (March 15, 2012). "Japanese Avengers trailer is stuffed with new footage". Total Film.
Jump up ^ "This week's cover: 'Iron Man 2' with exclusive photos!" Entertainment Weekly. July 16, 2009
Jump up ^ Ridgely, Charlie (January 26, 2018). "Avengers: Infinity War': Gwyneth Paltrow Lets Some Pepper Potts Spoilers Slip". Comicbook.com. Archived from the original on January 26, 2018. Retrieved January 26, 2018.
Jump up ^ Wilson, Matt D. (November 27, 2013). "Take A Look At The Superheroines Of ‘Marvel Universe Live!’" Archived 2014-07-17 at the Wayback Machine.. Comics Alliance.
External links[edit]
Pepper Potts at Marvel.com
Virginia 'Pepper' Potts at the Comic Book DB
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