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Coulomb's Law

The electric force acting on a point charge.

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coulombs law - force

Coulomb's law calculates the electric force acting between to electric charges q 1 and q 2and can be expressed as

F = k q 1 q2/ r2

= q 1 q2/ (4 π ε 0 r2)    (1)


F = force of attraction or repulsion (N)

k = Coulomb's constant = 1 / (4 π ε 0 ) = 8.9875517873681764 × 10 9 (Nm2/C2) in air

q = charge (Coulombs, C)

r = distance between charges (m)

ε 0 = permittivity of space or vacuum

The quantity of charge (number of electrons) is measured in the unit Coulomb - C - where

1 coulomb (C) = 6.24 1018 electrons

The smallest charge that exists is the charge carried by an electron equal to -1.602 10-19 coulomb .

Example - Force between two Charged Bodies

Two spheres in air with distance 20 mm is both charged with 2 μC (2 10-6 C) . The force acting between the two spheres can be calculated as

F = ( 8.98755 10 9 Nm2/C2) ( (2 μC ) (10-6 C/ μC )) ( (2 μC ) (10-6 C/ μC )) / ((20 mm)(10 -3 m/mm))2

= 90 N

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