A conductor $10 \mathrm{~cm}$ long is moved with a speed $1 \mathrm{~m} / \mathrm{s}$ perpendicular to a…

A conductor $10 \mathrm{~cm}$ long is moved with a speed $1 \mathrm{~m} / \mathrm{s}$ perpendicular to a field of strength 1000 $\mathrm{A} / \mathrm{m}$. The e.m.f. induced in the conductor is [Given : $\mu_0=4 \pi \times 10^{-7} \mathrm{~Wb} / \mathrm{Am}$ ]
  1. $\pi \mathrm{mV}$
  2. $2 \pi \mathrm{mV}$
  3. $40 \pi \mu \mathrm{V}$
  4. $4 \pi \mu \mathrm{V}$

Solution

Motional emf $\mathrm{e}=\mathrm{Bv} \mathrm{l}$ Magnetic field $B=\mu_0 H$ $\therefore \quad \mathrm{e}=\mu_0 \mathrm{H} \mathrm{v} l$ $\begin{aligned} & \mathrm{e}=4 \pi \times 10^{-7} \times 1000 \times 0.01 \times 1 \\ & \mathrm{e}=40 \pi \mu \mathrm{V}\end{aligned}$

Asked in: MHT CET 2023 (13 May Shift 2)

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