JEE Advanced 2021 Paper 2 Q04 Physics Errors & Measurements Dimensional Analysis Medium

JEE Advanced 2021 Paper 2 · Q04 · Dimensional Analysis

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)?

  1. A. $\dfrac{\text{Energy}}{\text{Charge} \times \text{Current}}$
  2. B. $\dfrac{\text{Force}}{\text{Length} \times \text{Time}}$
  3. C. $\dfrac{\text{Energy}}{\text{Volume}}$
  4. D. $\dfrac{\text{Power}}{\text{Area}}$
JEE Advanced multi-correct — pick every correct option, then check.
Reveal answer + step-by-step solution

Correct answer:B, D

Solution

$\vec{S} = \vec{E}\times\vec{B}/\mu_0$ is the Poynting vector — energy flux per unit area per unit time, SI units W/m$^2$ = J s$^{-1}$ m$^{-2}$. Dimensions $[S] = MT^{-3}$. Check: (A) Energy/(Charge$\cdot$Current) $= ML^2T^{-2}/(AT \cdot A) = ML^2T^{-3}A^{-2}$ — wrong (this is resistance$\cdot$length$^2$/something else). (B) Force/(Length$\cdot$Time) $= MLT^{-2}/(L \cdot T) = MT^{-3}$ — matches. (C) Energy/Volume $= ML^{-1}T^{-2}$ — wrong (pressure). (D) Power/Area $= ML^2T^{-3}/L^2 = MT^{-3}$ — matches.

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