A plane loop is shaped as two squares (figure) and placed in a uniform magnetic field at right angle to the loop's plane. The magnetic induction varies with time as $$B=B0$$ $$sin$$ ωt, where $$B0=10$$ mT and ω $$=$$ $$100$$ $$rads-1$$. The wires do not touch at point A. If resistance per unit length of the loop is $$50m$$Ω$$/m$$, then amplitude of current induced in the loop is

Question

A plane loop is shaped as two squares (figure) and placed in a uniform magnetic field at right angle to the loop's plane. The magnetic induction varies with time as $$B=B0$$ $$sin$$ ωt, where $$B0=10$$ mT and ω $$=$$ $$100$$ $$rads-1$$. The wires do not touch at point A. If resistance per unit length of the loop is $$50m$$Ω$$/m$$, then amplitude of current induced in the loop is

Infinity Learn · Accepted Answer

Induced emf's in the two loops will oppose each other. So net induced emf:$$e=ddtb2-a2B=b2-a2dBdt=0.202-0.102$$ω$$B0$$ $$cos$$ ω$$t=0.04-0.01$$×$$100$$×$$10$$×$$10-3$$ $$cos$$ ω$$t=30$$×$$10-3$$ $$cos$$ ωtResistance: $$R=50$$×$$10-34$$×$$0.20+4$$×$$0.10=60$$×$$10-3$$Ω$$I=eR=0.5$$ $$cos$$ ωtSo amplitude of current $$=$$ $$0.5$$ A

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