Q.

In fig, CODF is a semicircular loop of a conducting wire of resistance R and radius r. It is placed in a uniform magnetic field B, which is directed into the page (perpendicular to the plane of the loop).The loop is rotated with a constant angular speed ω about an axis passing through the centre O, and perpendicular to the page. Then the induced current in the wire loop is

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a

zero

b

Br2ω/R

c

Br2ω/2R

d

Bπr2ω/R

answer is C.

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Detailed Solution

The area swept by radius OC in one half circle is πr2/2 . The flux change in  time T/2 is thus (πr2 B/2) . The induced emf is then e=πr2 B/T=Bωr2/2[∵T=2πω] The induced current is then I=e/R=Bωr2/2R
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In fig, CODF is a semicircular loop of a conducting wire of resistance R and radius r. It is placed in a uniform magnetic field B, which is directed into the page (perpendicular to the plane of the loop).The loop is rotated with a constant angular speed ω about an axis passing through the centre O, and perpendicular to the page. Then the induced current in the wire loop is