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## Encyclopedia > Coulomb's Law

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# Coulomb's law

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In physics, Coulomb's Law is an inverse-square law indicating the magnitude and direction of electrical force that one stationary, electrically charged substance of small volume exerts on another. When one is interested only in the magnitude of the force (and not in its direction), it may be easiest to consider a simplified, scalar version of the Law

$F = \frac{\left|q_1 q_2\right|}{4 \pi \epsilon_0 r^2}$

where q1 is the charge on one substance, q2 is the charge on the other, r is the distance between them, and ε0 is a universal constant, the permittivity of vacuum. (See physical constants for more information. Note that 1/(μ0ε0) = c2 × 10-7, where μ0 is the permeability of vacuum and c is the speed of light.)

Among other things, this formula says that the magnitude of the force is directly proportional to the magnitude of the charges of each substance and inversely proportional to the square of the distance between them.

The force F acts on the line connecting the two charged objects.

For calculating the direction and magnitude of the force simultaneously, one will wish to consult the full-blown vector version of the Law

$\mathbf{F} = \frac{q_1 q_2 \mathbf{r}}{4 \pi \epsilon_0 \left|\mathbf{r}\right|^3}$

where the vector r connects the two substances, and the other symbols are as before.

(The r vector in the numerator indicates that the force should be along the vector connecting the two substances. |r| has been raised to the third power instead of the second in the denominator in order to normalize the length of the r in the numerator to 1.)

In either formulation, Coulomb's Law is fully accurate only when the substances are static (i.e. stationary), and remain approximately correct only for slow movement. When movement takes places, magnetic fields are produced that alter the force on the two substances. Especially when rapid movement takes place, the electric field will also undergo a transformation described by Einstein's theory of relativity.

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