Using mass `(M)` , length `(L)` , time `(T)` , and electric current `(A)` as fundamental quantities , the dimensions of permitivity will be

Options

A. `[in_0]= M^(-1) L^(-3) T^2 A`
B. `[in_0] = M^(-1) L^(-3) T^4 A^2`
C. `[in_0] = MLT^(-2) A(-2)`
D. `[in_0] = ML^2 T^(-1)A`

Answer

(b)

Explanation

From Coulomb's law, `F = (q_1 q_2)/(4 pi in_0 r^2)`
`in_0 =(q_1q_2)/(4pi F r^2) = ((AT)(AT))/((MLT^(-2))L^2) = [M^(-1) L^(-3) T^4 A^2]`
Choice (b) is correct.