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Q.

The magnetic field in a region is given by B⇀=k∧B0Ly where L is a fixed length. A conducting rod of length L lies along the Y-axis between the origin and the point (0, L,0). If the rod moves with a velocity v⇀=v0i∧, find the emf induced between the ends of the rod.

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a

2B0v0l

b

B0v0l

c

B0v0l2

d

None of these

answer is C.

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Detailed Solution

Consider an element of width dy at a distance y from origin.Induced emf across its ends is Bv0dy. where B=B0LyIntegrating from 0 to L, ∫dε=∫0lB0v0ydyL ε=B0v0l2

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The magnetic field in a region is given by B⇀=k∧B0Ly where L is a fixed length. A conducting rod of length L lies along the Y-axis between the origin and the point (0, L,0). If the rod moves with a velocity v⇀=v0i∧, find the emf induced between the ends of the rod.