A square metallic wire loop of side $$0.1$$ m and resistance of $$1$$Ω is moved with a constant velocity in a magnetic field of $$2$$ $$wb/m2$$ as shown in figure. The magnetic field is perpendicular to the plane of the loop, loop is connected to a network of resistances. What should be the velocity of loop so as to have a steady current of $$1mA$$ in loop

Question

A square metallic wire loop of side $$0.1$$ m and resistance of $$1$$Ω is moved with a constant velocity in a magnetic field of $$2$$ $$wb/m2$$ as shown in figure. The magnetic field is perpendicular to the plane of the loop, loop is connected to a network of resistances. What should be the velocity of loop so as to have a steady current of $$1mA$$ in loop

Infinity Learn · Accepted Answer

Equivalent resistance of the given Wheatstone bridge circuit (balanced) is $$3$$Ω so total resistance in circuit is  $$R=3+1=4$$Ω. The emf induced in the loop $$e=Bvl$$ .So induced current  $$i=eR=BvlR$$   ⇒   $$10$$−$$3=2$$×v×$$(10$$×$$10$$−$$2)4$$⇒$$v=2cm/$$$$sec$$.

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