Questions

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

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2B0v0l

B0v0l

B0v0l2

None of these

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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

Similar Questions

An elasticized conducting band r is around a spherical balloon T (figure). Its plane passes through the center of the balloon. A uniform magnetic field of magnitude 0.04 T is directed perpendicular to the plane of the band. Air is let out of the balloon at 100 cm³s^-1 at an instant when the radius of the balloon is 10 cm. The induced emf in the band is