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Physics Question on physical world

In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, [E][E] and [ The relation between [ε0][\varepsilon_0] and [μ0][\mu_0] is

A

[μ0]=[ε0][L]2[T]−2[\mu_0] = [\varepsilon_0] [L]^2 [T]^{-2}

B

[μ0]=[ε0][L]−2[T]2[\mu_0] = [\varepsilon_0] [L]^{-2} [T]^{2}

C

[μ0]=[ε0]−1[L]2[T]2[\mu_0] = [\varepsilon_0]^{-1} [L]^2 [T]^{2}

D

[μ0]=[ε0]−1[L]−2[T]2[\mu_0] = [\varepsilon_0]^{-1} [L]^{-2} [T]^{2}

Answer

[μ0]=[ε0]−1[L]−2[T]2[\mu_0] = [\varepsilon_0]^{-1} [L]^{-2} [T]^{2}

Explanation

Solution

We have,
C=1μ0∈0C = \frac{1}{\sqrt{\mu_{0} \in_{0}}}
∴[C2]=[1μ0∈0]\therefore \left[C^{2}\right] = \left[\frac{1}{\mu_{0 } \in_{0}}\right]
⇒L2T−2=1[μ0][∈0]\Rightarrow L^{2}T^{-2} = \frac{1}{\left[\mu_{0}\right]\left[\in_{0}\right]}
⇒[μ0]=[∈0]−1[L]−2[T]2\Rightarrow \left[\mu_{0}\right] = \left[\in_{0}\right]^{-1} \left[L\right]^{-2} \left[T\right]^{2}