The dimensional formula of frac{1}{2} mu_0 H^ | vedclass

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(C) The expression $\frac{1}{2} \mu_0 H^2$ represents the energy density of a magnetic field.Energy density is defined as energy per unit volume.The d

Vedclass · Accepted Answer

$[ML^{-1} T^{-2}]$

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(C) The expression $\frac{1}{2} \mu_0 H^2$ represents the energy density of a magnetic field.Energy density is defined as energy per unit volume.The dimensional formula for energy is $[ML^2 T^{-2}]$ and for volume is $[L^3]$.Therefore,the dimensional formula for energy density is $\frac{[ML^2 T^{-2}]}{[L^3]} = [ML^{-1} T^{-2}]$.Alternatively,using the dimensions of $\mu_0$ and $H$:$[\mu_0] = [MLT^{-2} A^{-2}]$ and $[H] = [AL^{-1}]$.Substituting these into the expression: $[\mu_0 H^2] = [MLT^{-2} A^{-2}] 	imes [AL^{-1}]^2 = [MLT^{-2} A^{-2}] 	imes [A^2 L^{-2}] = [ML^{-1} T^{-2}]$.

Column-$I$	Column-$II$
$1. m = -2$	$a$. Convex mirror
$2. m = -\frac{1}{2}$	$b$. Concave mirror
$3. m = +2$	$c$. Real Image
$4. m = +\frac{1}{2}$	$d$. Virtual image

The dimensional formula of $\frac{1}{2} \mu_0 H^2$ (where $\mu_0 = \text{permeability of free space}$ and $H = \text{magnetic field intensity}$) is:

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