The dimensions of `mu_(0)I//MB` where `mu_(0)` is the permeability of free space, I is the moment of inertia, M is the magnetic moment and B is the magnetic induction respectively, are those of

Options

A. time
B. `("time")^(2)`
C. `("time")^(3)`
D. `("time")^((1)/(2))`

Answer

B

Explanation

`B= mu_(0)ni` (For a solenoid)
where n is the number of turns per unit length , I is the current and `mu_(0)` is the permeability of free space.
or `(mu_(0))/(B) = (1)/(ni) :. [(mu_(0))/(B)]= [(1)/(ni)]= (1)/([L^(-1)][A])= [LA^(-1)]`
`[M]= ["Magnetic moment"]= [ m xx 2l]`
[pole strenght `xx` magnetic lenght]
`=["weber xx L] = [ML^(2)T^(-2)A^(-1)xx L]= [ML^(3)T^(-2)A^(-1)]`
`= [LA^(-1)] xx ([ML^(2)])/([ML^(3)T^(-2)A^(-1)])= [T^(2)]= ("time")^(2)`