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The magnetic field inn a region is given...

The magnetic field inn a region is given by `vec B = veck (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 `v= v_0` , find the emf induced between the ends of the rod.

A

`2 B_(0)v_(0)l`

B

`(B_(0)v_(0)l`

C

`(B_(0)v_(0)l)/(2)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Consider an element of width dy at a distance y form origin.
Induced emf across its ends is `Bv_(0)dy`, where `B=(B_(0))/(L) y`.
Intergrating from 0 to L, `E=(B_(0)v_(0)l)/(2)`.
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