Q.A metal rod AB of length L is placed in a magnetic field as shown in the figure.If the rate of change of B w.r.t time is dB/dt,find the emf produced across AB.

Please help me in solving these types of problems.

Dear Raj,

MY PREVIOUS SOLUTION WAS COMPLETELY INCORRECT. PLEASE IGNORE IT.

Consider a square metal loop of side L whose plane is perpendicular to dB/dt.

Induced emf=area*dB/dt=L²dB/dt,

therefore emf induced across AB=(L²/4)dB/dt

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CHETAN MANDAYAM NAYAKAR

THE CORRECT ANSWER IS (1/4)L²a·(dB/dt)

a is the unit vector perpendicular to the square loop considered in the previous solution to this problem.