A rectangular conducting loop of sides 8, cm | vedclass

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(C) The motional electromotive force $(EMF)$ induced in a conductor moving in a magnetic field is given by $V = B \ell v$,where $\ell$ is the length o

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$4$

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(C) The motional electromotive force $(EMF)$ induced in a conductor moving in a magnetic field is given by $V = B \ell v$,where $\ell$ is the length of the conductor perpendicular to both the magnetic field $B$ and the velocity $v$.In case $(i)$,the side of length $\ell = 8\, cm$ is moving perpendicular to the magnetic field. Thus,the voltage developed across $ab$ is $V_1 = B \ell v = B(8\, cm)v$.In case $(ii)$,the side of length $b = 2\, cm$ is moving perpendicular to the magnetic field. Thus,the voltage developed across $ab$ is $V_2 = B b v = B(2\, cm)v$.The ratio of the voltage in case $(i)$ to case $(ii)$ is:$\frac{V_1}{V_2} = \frac{B(8\, cm)v}{B(2\, cm)v} = \frac{8}{2} = 4$.

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