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A conducting rod of length 1 is moving o...

A conducting rod of length 1 is moving on a horizontal smooth surface. Magnetic field in the region is vertically downward and magnitude `B_(0)`. If centre of mass (COM) of the rod is translating with velocity `v_(0)` and rod rotates about COM with angular velocity `v_(0)//l`, then potential difference between points O and A will be

A

`5/8 B_(0)v_(0)l`

B

`3/8 B_(0)v_(0)l`

C

`1/8 B_(0)v_(0)l`

D

`1/2 B_(0)v_(0)l`

Text Solution

Verified by Experts

The correct Answer is:
A
`v=v_(0)+wx=v_(0)+(v_0)/(l)x` due to mutual induction
`int de = int B vdx`
`e=int_(0)^(l//2) B(v_(0)+(v_(0)x)/(l))dx = 5/8 B_(0)v_(0)l`
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