First slide
Motional EMF
Question

A rectangular loop with a sliding connector of Iength 10 cm is situated in a uniform magnetic field perpendicular to plane of loop. The magnetic induction is 0.1 T and resistance of connector (R) is 1 ohm. The sides AB and CD have resistances 2 ohm and 3 ohm respectively. Find the current in the connector during its motion with constant velocity one metre/sec.

Difficult
Solution

When the connector moves through a distance x, then area covered = I x
flux linked = B l x = ϕ
Induced e.m.f., e=dt=Bldxdt=Blv
This acts as a cell of e.m.f. B I v and internal resistance fl. Effective resistance of the circuit
=R1R2R1+R2
Total resistance of the circuit
=R+R1R2R1+R2
current i=BlvR+R1R2R1+R2
=01×110×11+(2×3)(2+3)=1220A

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