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(B) The motional electromotive force (e.m.f.) induced in a conductor moving through a magnetic field is given by the formula $\varepsilon = B l v$,whe

Vedclass · Accepted Answer

$({e_c} = {e_d}) > ({e_a} = {e_b})$

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(B) The motional electromotive force (e.m.f.) induced in a conductor moving through a magnetic field is given by the formula $\varepsilon = B l v$,where $B$ is the magnetic field strength,$l$ is the length of the conductor perpendicular to the velocity vector,and $v$ is the velocity.In this case,the loops move horizontally into the magnetic field. The vertical sides of the loops act as the moving conductors that cut the magnetic field lines.Let $l$ be the vertical length of the loop. The induced e.m.f. is proportional to this vertical length $l$.From the figure,loops $c$ and $d$ have a vertical side length of $2L$,while loops $a$ and $b$ have a vertical side length of $L$.Since the velocity $v$ and magnetic field $B$ are the same for all loops,the induced e.m.f. $\varepsilon$ is greater for loops with a larger vertical side length.Therefore,$\varepsilon_c = \varepsilon_d = B(2L)v$ and $\varepsilon_a = \varepsilon_b = B(L)v$.Comparing these,we get $(\varepsilon_c = \varepsilon_d) > (\varepsilon_a = \varepsilon_b)$.

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