The dimensional formula for the physical quan | vedclass

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Question

(A) We know that the speed of light $c$ is related to the permeability of free space $\mu_0$ and permittivity of free space $\varepsilon_0$ by the rel

Vedclass · Accepted Answer

$L^0M^0T^0$

Vedclass · Answer

(A) We know that the speed of light $c$ is related to the permeability of free space $\mu_0$ and permittivity of free space $\varepsilon_0$ by the relation: $\mu_0 \varepsilon_0 = \frac{1}{c^2}$.Also,the ratio of the magnitude of the electric field $E$ to the magnetic field $B$ in an electromagnetic wave is equal to the speed of light: $\frac{E}{B} = c$.Substituting these into the given expression:$\frac{E^2 \mu_0 \varepsilon_0}{B^2} = \left( \frac{E}{B} \right)^2 (\mu_0 \varepsilon_0) = (c)^2 \left( \frac{1}{c^2} \right) = 1$.The quantity is dimensionless.Therefore,the dimensional formula is $[M^0 L^0 T^0]$.

The dimensional formula for the physical quantity $\frac{E^2 \mu_0 \varepsilon_0}{B^2}$ is ($E =$ electric field and $B =$ magnetic field).

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