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 B→ is perpendicular to the plane of the loop. This loop is connected to a network of resistances. What should be the velocity of loop so as to have a steady current of $$1$$ mA 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 B→ is perpendicular to the plane of the loop. This loop is connected to a network of resistances. What should be the velocity of loop so as to have a steady current of $$1$$ mA 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×$$10-14$$⇒$$v=2$$ $$cm/s$$

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