Using mass (M), length (L), time (T) and current (A) as fundamental quantities, the dimension of permittivity is:

Options

A. `M^(-1)LT^(-2)A`
B. `ML^2T(-2)A^(-1)`
C. `MLT^(-2)A^(-2)`
D. `MLT(-1)A^(-1)`

Answer

C

Explanation

We know that the force per unit length of a wire carrying due to another parallel wire carrying current is given by
`(dF)/(dl)=(mu_0i_1i_2)/(2pid) rArr mu_0=(2pid)/(i_1i_2)(dF)/(dl)`
`therefore [mu_0]=([L])/([A^2]).([MLT^(-2)])/([L])`
or `[mu_0]=[MLT^(-2)][A^(-2)]=[MLT^(-2)A^(-2)]`