JEE Advanced 2018 · Paper 1 · Physics Q15

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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 $[\epsilon_0]$ and $[\mu_0]$ stand for dimensions of the permittivity and permeability of free space respectively. $[L]$ and $[T]$ are dimensions of length and time respectively. All the quantities are given in SI units.

The relation between $[E]$ and $[B]$ is

[E] = [B]\,[L]\,[T]

[E] = [B]\,[L]^{-1}\,[T]

[E] = [B]\,[L]\,[T]^{-1}

[E] = [B]\,[L]^{-1}\,[T]^{-1}

Answer and worked solution

Official answer: C

In an electromagnetic wave $E=cB$ , so $[E]=[B][\text{velocity}]$ :
$[E]=[B][L][T]^{-1}.$
(Alternatively, $\vec F=q\vec E=q\vec v\times\vec B$ gives the same.)

(C)

Topics:Dimensional analysis Properties of EM waves

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JEE Advanced 2018 · Paper 1, Physics question 15