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Which of the following is the correct unit of proportionality constant ( $K$ ) in Coulomb’s law?

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N m^{2}

N

N C^{2}

m^{2}

{N m}^{2}

C^{2}

answer is D.

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Detailed Solution

The unit of proportionality constant (

K

) in Coulomb’s law is

{N m}^{2}

C^{2}

.
The force between two opposite charges

q_{1,} q_{2}

is F, and the distance between them is r. According to Coulomb’s law, the force between them is given by

F = \frac{K q_{1} q_{2}}{r^{2}}

, So, the constant of proportionality is calculated as,

K = \frac{F r^{2}}{q_{1} q_{2}}

. We know that the unit of force in

N (newton)

, unit of charge is

C (coulomb)

and unit of distance is

m (metre)

, so the unit of proportionality constant

K

becomes

N m^{2} / C^{2}

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