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The dimensions of $\frac{B^{2}}{2 \mu_{0}}$, where $B$ is magnetic field and $\mu_{0}$

is the magnetic permeability of vacuum, is:

  1. $\mathrm{MLT}^{-2}$

  2. $\mathrm{ML}^{2} \mathrm{~T}^{-1}$

  3. $\mathrm{ML}^{2} \mathrm{~T}^{-2}$

  4. $\mathrm{ML}^{-1} \mathrm{~T}^{-2}$

Correct Option: , 4


(4) The quantity $\frac{\mathrm{B}^{2}}{2 \mu_{0}}$ is the energy density of magnetic field.

$\Rightarrow\left[\frac{B^{2}}{2 \mu_{0}}\right]=\frac{\text { Energy }}{\text { Volume }}=\frac{\text { Force } \times \text { displacement }}{(\text { displacement })^{3}}$

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

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