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

Options

A. `[M LT^(-1) A^(-1)]`
B. `[M LT^(-2) A^(-2)]`
C. `[M^(-1) L^(-3) T^(4) A^(2)]`
D. `[M^(2) L^(-2) T^(-2) A]`

Answer

C

Explanation

By Coulomb's laws `F = (1)/(4 pi epsilon_(0))xx(q_(1)q_(2))/(r^(2))`
`epsilon_(0)=(q_(1)q_(2))/(4 pi xx F xx r^(2))`
Taking dimensions
`epsilon_(0)=((AT)(AT))/(ML^(1)T^(-2)xxL^(2))=(M^(-1)L^(-3)T^(4)A^(2)]`.