A wire of length ' $L$ ' having resistance ' $R$ ' falls from a height ' $\ell$ ' in earth's horizontal…

A wire of length ' $L$ ' having resistance ' $R$ ' falls from a height ' $\ell$ ' in earth's horizontal magnetic field ' $\mathrm{B}$ '. The induced emf through the wire is ( $\mathrm{g}$ = acceleration due to gravity)
  1. $\mathrm{BL} \sqrt{2 \mathrm{~g} \ell}$
  2. $\frac{\mathrm{BL} \sqrt{2 \mathrm{~g} \ell}}{2}$
  3. $\frac{\mathrm{BL} \sqrt{2 \mathrm{~g} \ell}}{\mathrm{R}}$
  4. $\frac{\mathrm{BL}}{\sqrt{2 \mathrm{~g} \ell}}$

Solution

If the wire falls through a height $\ell$, the velocity acquired by it is $\mathrm{v}=\sqrt{2 \mathrm{~g} \ell}$ The emf induced in the wire $\mathrm{E}=\mathrm{BLv}=\mathrm{BL} \sqrt{2 \mathrm{~g} \ell}$

Asked in: MHT CET 2021 (21 Sep Shift 1)

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