If is the permittivity of free space and E is the electric field, then has the dimensions

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Solution

Q.
If $\in_{0}$ is the permittivity of free space and E is the electric field, then $\in_{0} E^{2}$ has the dimensions [2024]

1 $[M^{0} L^{- 2} T A]$

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

3 $[M^{- 1} L^{- 3} T^{4} A^{2}]$

4 $[M L^{2} T^{- 2}]$

Ans.
(2)

Energy per unit volume = $\frac{1}{2} \in_{0} E^{2}$

$\frac{1}{2} \in_{0} E^{2} \Rightarrow [M L^{- 1} T^{- 2}] = \in_{0} E^{2}$

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