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Question

The magnetic field in a region is given by B=3r, where r is the distance from the origin. The direction of the magnetic field is along the negative z-axis. A conducting rod of length 20 cm lies as shown in the figure. If the rod is rotating with an angular velocity of 4 rad/s, find the emf induced between the ends of the rod.


A
1.6×102 V
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B
3.2×102 V
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C
6×102 V
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D
4×102 V
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Solution

The correct option is B 3.2×102 V
Consider an element of length dr at a distance r.


Emf induced in this element is:

dE=Bvl=B(ωr)dr

dE=3r×4×r dr=12r2dr

Total emf developed across the ends of the rod is,

E=dE=0.2012r2 dr

=12×[r33]0.20=4×(0.2)3

E=3.2×102 V

Hence, (B) is the correct answer.

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