Question

Medium

Solving time: 3 mins

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, $[E]$ and [B] stand for dimensions of electric and magnetic fields respectively, while $\left[{\epsilon }_0\right]$ and $\left[{\mu }_0\right]$ stand for dimensions of the permittivity and permeability of free space, respectively. $[\mathrm{L}]$ and $[\mathrm{T}]$ are dimensions of length and time, respectively. All the quantities are given in SI units.
1. The relation between $[E]$ and $[B]$ is

(a) $[E]=[B][\mathrm{L}][\mathrm{T}]$
(b) $[E]=[B][L{]}^{-1}[\mathrm{T}]$
(c) $[E]=[B][L][T{]}^{-1}$
(d) $[E]=[B][L{]}^{-1}[T{]}^{-1}$
2. The relation between $\left[{\epsilon }_0\right]$ and $\left[{\mu }_0\right]$ is
(a) $\left[{\mu }_0\right]=\left[{\epsilon }_0\right][L{]}^2[T{]}^{-2}$
(b) $\left[{\mu }_0\right]=\left[{\epsilon }_0\right][L{]}^{-2}[T{]}^2$
(c) $\left[{\mu }_0\right]={\left[{\epsilon }_0\right]}^{-1}[L{]}^2[T{]}^{-2}$
(d) $\left[{\mu }_0\right]={\left[{\epsilon }_0\right]}^{-1}[L{]}^{-2}[T{]}^2$

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Updated on: Apr 26, 2023

Book:

Mechanics Volume 1 (DC Pandey)