Questions

The magnetic field in a region is given by $\stackrel{⇀}{B}=\stackrel{\wedge }{k}\frac{{B}_{0}}{L}y$ 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 $\stackrel{⇀}{v}={v}_{0}\stackrel{\wedge }{i}$, find the emf induced between the ends of the rod.

a
2B0v0l
b
B0v0l
c
B0v0l2
d
None of these

detailed solution

Correct option is C

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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