The dimension of $\frac{B^{2}}{2 \mu_{0}}$, where $B$ is magnetic field and $\mu_{0}$ is the magnetic permeability of vacuum, is

(C) $\mathrm{ML}^{-1} \mathrm{~T}^{-2}$

(A) $\mathrm{ML}^{2} \mathrm{~T}^{-1}$

(B) $\mathrm{ML}^{2} \mathrm{~T}^{-2}$

JEE Main · 2020 · 07 Jan 2020 · Shift 2 · Units & Measurement

The dimension of

\frac{B ^{2}}{2 μ _{0}}

, where

B

is magnetic field and

μ_{0}

is the magnetic permeability of vacuum, is

Answer: (C)

The expression

\frac{B ^{2}}{2 μ _{0}}

is the energy stored per unit volume in a magnetic field, so its dimensions are just those of energy divided by volume. Energy carries the dimensions

[M L^{2} T^{- 2}]

and volume carries

[L^{3}]

, and dividing one by the other leaves

\frac{[ M L ^{2} T ^{- 2} ]}{[ L ^{3} ]} = [M L^{- 1} T^{- 2}]

JEE Main · 2020 · 07 Jan 2020 · Shift 2 · Single correct option