Dimensions of frac{1}{{mu _0 varepsilon _0}}, | vedclass

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Question

(D) The speed of light in vacuum is given by the relation $c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}$.Squaring both sides,we get $c^2 = \frac{1}{\mu_0

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) The speed of light in vacuum is given by the relation $c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}$.Squaring both sides,we get $c^2 = \frac{1}{\mu_0 \varepsilon_0}$.Since $c$ represents the speed of light,its dimensions are $[L T^{-1}]$.Therefore,the dimensions of $\frac{1}{\mu_0 \varepsilon_0}$ are the dimensions of $c^2$,which is $[L T^{-1}]^2 = [L^2 T^{-2}]$.Thus,the correct option is $D$.

Column-$I$	Column-$II$
$(A)$ Electrical resistance	$(p)$ $M L^3 T^{-3} A^{-2}$
$(B)$ Electrical potential	$(q)$ $M L^2 T^{-3} A^{-2}$
$(C)$ Specific resistance	$(r)$ $M L^2 T^{-3} A^{-1}$
$(D)$ Specific conductance	$(s)$ None of these

Dimensions of $\frac{1}{{\mu _0 \varepsilon _0}}$,where symbols have their usual meaning,are:

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Column-$I$ Column-$II$

$(A)$ Electrical resistance $(p)$ $M L^3 T^{-3} A^{-2}$

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$(C)$ Specific resistance $(r)$ $M L^2 T^{-3} A^{-1}$

$(D)$ Specific conductance $(s)$ None of these

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