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JEE Main 20252 AprilEvening Shift
Exam
JEE Main
Year
2025
Date
2 April
Shift
Evening Shift
Subject
Physics
Chapter
Units and Dimensions

JEE Main 2025 · 2 April · Evening Shift · Physics · Units and Dimensions

Given a charge q , current I and permeability of vacuum μ_0 . Which...

Given a charge qq, current I and permeability of vacuum μ0\mu_0. Which of the following quantity has the dimension of momentum?

Options

  1. AqI/μ0\mathrm{qI} / \mu_0
  2. Bqμ0Iq \mu_0 I
  3. Cq2μ0Iq^2 \mu_0 I
  4. Dqμ0/Iq \mu_0 / I

Correct answer

B. qμ0Iq \mu_0 I

Step-by-step solution

Q=ATI=Aμ0=MLT−2A−2P=Qxμ0yIz=[AT]x[MLT−2A−2]y[A]zMLT−1=MyLyTx−2yA−2y+z+x Now; y=1x−2y=−1−2y+z=0∴x=y=z=1\begin{aligned} & \mathrm{Q}=\mathrm{AT} \\ & \mathrm{I}=\mathrm{A} \\ & \mu_0=\mathrm{MLT}^{-2} \mathrm{ A}^{-2} \\ & \mathrm{P}=\mathrm{Q}^{\mathrm{x}} \mu_0^{\mathrm{y}} \mathrm{I}^{\mathrm{z}}=[\mathrm{AT}]^{\mathrm{x}}\left[\mathrm{MLT}^{-2} \mathrm{ A}^{-2}\right]^{\mathrm{y}}[\mathrm{A}]^{\mathrm{z}} \\ & \mathrm{MLT}^{-1}=\mathrm{M}^{\mathrm{y}} \mathrm{L}^{\mathrm{y}} \mathrm{T}^{\mathrm{x}-2 \mathrm{y}} \mathrm{A}^{-2 \mathrm{y}+\mathrm{z+x}} \\ & \text{ Now; } \mathrm{y}=1 \\ & \mathrm{x}-2 \mathrm{y}=-1 \\ & -2 \mathrm{y}+\mathrm{z}=0 \\ & \therefore \mathrm{x}=\mathrm{y}=\mathrm{z}=1\end{aligned}
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