Q.

A thin conducting rod of length l = 5m is moved such that its end B moves along the X-axis while end A moves along the Y-axis. An uniform magnetic field B=6k^T exists in the region. At some instant, velocity of end B is 3 ms-1 and the rod makes an angle of θ =37° with the X-axis as shown in the figure. Then, at this instant, if emf induced in the rod is 'ε' then, find value of ε/3 (in volts).

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answer is 7.

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Detailed Solution

ε=BVcm×L=(6k^)32i^42j^×(4i^+3j^)=21/3=7V.

Alternate method:

On considering the area under the rod

ε=dϕdt=B.dx.ydt=Bx.dydt+ydxdt

here dydt=-4m/s, dxdt=3m/s

on substituting the values we get ε=21V

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