Question

Find the dimensions of $\frac{B^2}{{\mu }_0}$ (B = Magnetic field, ${\mu }_0$ = magnetic permeability).

• A. $M^1{L}^{-1}{T}^{-2}$
• B. $M^1{L}^{-1}{T}^{-1}$
• C. $M^1{L}^1{T}^{-2}$
• D. $M^{-1}{L}^{-1}{T}^{-2}$

Answer 1

Answer: (A)

$M^1{L}^{-1}{T}^{-2}$

$\frac{1B^2}{2{\mu }_0}$ = Magnetic energy density

$\left[\frac{1}{2}\frac{B^2}{{\mu }_0}\right]$ = [Magnetic Energy density] $\Rightarrow$ $\left[\frac{B^2}{{\mu }_0}\right]=\frac{\left[energy\right]}{\left[volume\right]}=\frac{M^1{L}^2{T}^{-2}}{L^3}=M^1{L}^{-1}{T}^{-2}$