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# Coulomb's Law

## The electric force acting on a point charge.

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

F = k q 1 q 2 / r 2

= q 1 q 2 / (4 π ε 0 r 2 )    (1)

where

F = force of attraction or repulsion (N)

k = Coulomb's constant = 1 / (4 π ε 0 ) = 8.9875517873681764 × 10 9 (Nm 2 /C 2 ) 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 10 18 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 Nm 2 /C 2 ) ( (2 μC ) (10 -6 C/ μC )) ( (2 μC ) (10 -6 C/ μC )) / ((20 mm)(10 -3 m/mm)) 2

= 90 N

## Related Topics

• ### Electrical

Electrical units, amps and electrical wiring, wire gauge and AWG, electrical formulas and motors.

## Related Documents

• ### Relative Permittivity - the Dielectric Constant

Common materials and their relative permittivity.

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## Citation

• The Engineering ToolBox (2013). Coulomb's Law. [online] Available at: https://www.engineeringtoolbox.com/coulomb-law-electric-charge-force-d_1855.html [Accessed Day Month Year].

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2.19.10