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Which of the following is the correct unit of the proportionality constant in Coulomb’s law?

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N m^{2}

N

N C^{2}

m^{2}

{Nm}^{2}

C^{2}

answer is D.

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Detailed Solution

The correct unit of the proportionality constant in Coulomb’s law is

{Nm}^{2} / C^{2}

.
Let the force between two opposite charges

q_{1}

and

q_{2}

F

and the distance between them be

r

. According to Coulomb’s law of force between them is given by

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

. So, the constant of proportionality

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

. It is known that the SI unit of force is Newton

(N)

, the SI unit of charge is Coulomb

(C)

and the SI unit of distance is meter

(m)

, so the unit of proportionality constant

K

becomes

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

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