JEE Advanced 2021 · Paper 2 · Physics Q4

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PhysicsMultiple correct+4 / -2Question 4 of 57

A physical quantity $\vec S$ is defined as $\vec S = (\vec E \times \vec B)/\mu_0$ , where $\vec E$ is electric field, $\vec B$ is magnetic field and $\mu_0$ is the permeability of free space. The dimensions of $\vec S$ are the same as the dimensions of which of the following quantity(ies)?

\dfrac{\text{Energy}}{\text{Charge} \times \text{Current}}

\dfrac{\text{Force}}{\text{Length} \times \text{Time}}

\dfrac{\text{Energy}}{\text{Volume}}

\dfrac{\text{Power}}{\text{Area}}

Answer and worked solution

Official answer: B, D

Dimensions of $\vec S$ . $\vec S$ is the Poynting vector, power per unit area: $[S]=MT^{-3}$ .

Check each option.

(A) $\dfrac{\text{Energy}}{\text{Charge}\times\text{Current}}$ : $\dfrac{ML^2T^{-2}}{I^2T}=ML^2T^{-3}I^{-2}$ . No.
(B) $\dfrac{\text{Force}}{\text{Length}\times\text{Time}}$ : $\dfrac{MLT^{-2}}{LT}=MT^{-3}$ . Yes.
(C) $\dfrac{\text{Energy}}{\text{Volume}}$ : $ML^{-1}T^{-2}$ . No.
(D) $\dfrac{\text{Power}}{\text{Area}}$ : $MT^{-3}$ . Yes.

(B), (D)

Topics:Dimensional analysis Energy and momentum of EM waves

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JEE Advanced 2021 · Paper 2, Physics question 4