First slide
Magnetic flux and induced emf
Question

An equilateral triangular loop ADC having some resistance is pulled with a constant velocity v out of a uniform magnetic field directed into the paper (figure). At time t = 0, side DC of the loop is at edge of the magnetic field.

The induced current (i) versus time (t) graph will be as

Moderate
Solution

Let 2a be the side CD of the triangle and b be the length AE.

    AHAE=GHECGH=AHAEEC ⇒   GH=(bvt)ba=aabvt    FG=2GH=2aabvt     Induced emf, e=Bv(FG)=2Bvaabvt     Induced current, i=eR=2BvRaabvt or     i=k1k2t

Thus i-t graph is a straight line with negative slope and positive intercept.

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