The dimension of frac{B^{2}}{2 mu_{0}},where | vedclass

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Question

(A) The expression $\frac{B^{2}}{2 \mu_{0}}$ represents the magnetic energy density,which is the magnetic energy stored per unit volume.The formula fo

Vedclass · Accepted Answer

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

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(A) The expression $\frac{B^{2}}{2 \mu_{0}}$ represents the magnetic energy density,which is the magnetic energy stored per unit volume.The formula for energy density is $u = \frac{	ext{Energy}}{	ext{Volume}}$.The dimension of energy is $[M L^{2} T^{-2}]$ and the dimension of volume is $[L^{3}]$.Therefore,the dimension of energy density is $\frac{[M L^{2} T^{-2}]}{[L^{3}]} = [M L^{-1} T^{-2}]$.Thus,the dimension of $\frac{B^{2}}{2 \mu_{0}}$ is $[M L^{-1} T^{-2}]$.

List-$I$	List-$II$
$(A)$ Angular momentum	$(I)$ $[ML^2T^{-1}]$
$(B)$ Torque	$(II)$ $[ML^2T^{-2}]$
$(C)$ Stress	$(III)$ $[ML^{-1}T^{-2}]$
$(D)$ Pressure gradient	$(IV)$ $[ML^{-2}T^{-2}]$

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

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Match List-$I$ with List-$II$.

List-$I$ List-$II$

$(A)$ Angular momentum $(I)$ $[ML^2T^{-1}]$

$(B)$ Torque $(II)$ $[ML^2T^{-2}]$

$(C)$ Stress $(III)$ $[ML^{-1}T^{-2}]$

$(D)$ Pressure gradient $(IV)$ $[ML^{-2}T^{-2}]$

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