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Question

The magnetic field in a region is given by B=2r, where r is the perpendicular distance from the x-axis. The direction of the magnetic field is along the positive z -axis. A conducting rod of length 1 m lies parallel to the y-axis as shown in the figure. If the rod moves with the velocity v=8 m/s along the positive x-axis, find the emf induced between the ends of the rod.


A
48 V
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B
40 V
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C
35 V
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D
24 V
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Solution

The correct option is B 40 V
Given:
Consider a small element of length dr lying at a distance r from the x-axis.


Emf developed across this element is,

dE=Bvdr=2r×(8)×dr

Emf developed across the whole length of the rod is,

E=dE

=3216rdr=16[r22]32

=8×[94]=40 V

Hence, (B) is the correct answer.


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