A rectangular loop $\mathrm{PQMN}$ with movable arm $\mathrm{PQ}$ of length $12 \mathrm{~cm}$ and resistance…

A rectangular loop $\mathrm{PQMN}$ with movable arm $\mathrm{PQ}$ of length $12 \mathrm{~cm}$ and resistance $2 \Omega$ is placed in a uniform magnetic field of $0.1 \mathrm{~T}$ acting perpendicular to the plane of the loop as shown in figure. The resistance of the arms MN, NP and MQ are negligible. The current induced in the loop when arm $\mathrm{PQ}$ is moved with velocity $20 \mathrm{~ms}^{-1}$ is
  1. $0.12 \mathrm{~A}$
  2. $0.06 \mathrm{~A}$
  3. $0.24 \mathrm{~A}$
  4. $0.18 \mathrm{~A}$

Solution

$\mathrm{B}=0.1 \mathrm{~T}, \ell=0.12 \mathrm{~m}, \mathrm{v}=20 \mathrm{~m} / \mathrm{s}, \mathrm{R}=2 \Omega$ emf induced $\mathrm{e}=\mathrm{B} \ell \mathrm{v}=0.1 \times 0.12 \times 20=0.24 \mathrm{~V}$ $\mathrm{I}=\frac{\mathrm{V}}{\mathrm{R}}=\frac{0.24}{2}=0.12 \mathrm{~A}$ ^

Asked in: MHT CET 2021 (24 Sep Shift 2)

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