The dimension of `(B^2)/( 2mu_0)` , where B is magnetic field and `mu_0` is the magnetic permeability of vacuum is

Options

A. `M^(1) L^(-1) T^(-2)`
B. `M^(1) L^(2) T^(-2)`
C. `M^(1) L^(-1) T^(2)`
D. `M^(1) L^(-2) T^(-1)`

Answer

A

Explanation

Energy density due to magnetic field `= (B^2)/( 2mu_0)`
`("Force" xx" displacement")/("volume") = (B^2)/( 2mu_0) " "[because "Energy" = "Force" xx "displacement" ]`
`therefore [ (B^2) /( 2mu_0) ] = ([F][d])/([V]) " "[because 2mu_(0) " dimensionless" ]`
`(M^(1) L^(1) T^(-2) xx L^(1) )/( L^(3) )`
`= M^(1) L^(-1) T^(-2) `