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  • A rectangular loop of length and breadth b is situated in a uniform magnetic field of induction B with its plane perp

A rectangular loop of length \ell and breadth b is situated in a uniform magnetic field of induction B with its plane perpendicular to the field as shown in the figure. What is the induced e.m.f. if the loop is rotated with constant angular velocity \omega, about an axis passing through the centre parallel to the breadth through angle 180^{\circ} .

Option: 1

\mathrm{\frac{B \ell b \omega}{\pi}}


Option: 2

\mathrm{\frac{2 B \ell b \omega}{\pi}}


Option: 3

\mathrm{\frac{B \ell b \omega}{2 \pi}}


Option: 4

None


Answers (1)

best_answer

When the loop is rotated through180^{\circ} about an axis passing through centre and parallel to breadth then the change in magnetic flux

\mathrm{\mathrm{d} \phi=-\mathrm{B} \ell \mathrm{b}-(\mathrm{B} \ell \mathrm{b})=-2 \mathrm{~B} \ell \mathrm{b} .}

\mathrm{\therefore \text { The induced e.m.f. }}

\mathrm{\begin{aligned} & \mathrm{e}=-\frac{d \phi}{d t} \Rightarrow e=+\frac{2 B \ell b}{\left(\frac{\pi}{\omega}\right)} \\ & \Rightarrow e=\frac{2 B \ell b \omega}{\pi} \end{aligned}}

 

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