A circular ring, made of copper wire, has area of $$30$$ $$cm2$$ and resistance of $$10$$ Ω. It is placed in a uniform magnetic field of induction $$2$$ tesla with its plane perpendicular to the field. When the loop is rotated through an angle of θ about its diameter, $$3$$ x $$10-4$$ coulomb of charge flows through it. Then θ is

Question

A circular ring, made of copper wire, has area of $$30$$ $$cm2$$ and resistance of $$10$$ Ω. It is placed in a uniform magnetic field of induction $$2$$ tesla with its plane perpendicular to the field. When the loop is rotated through an angle of θ about its diameter, $$3$$ x $$10-4$$ coulomb of charge flows through it. Then θ is

Infinity Learn · Accepted Answer

ϕ$$1=AB=30$$×$$10$$−$$4$$×$$2$$ $$weber=6$$×$$10$$−$$3$$ weberϕ$$2=ABcos$$θ$$=6$$×$$10$$−$$3cos$$θNow charge flown, $$Q=$$ϕ$$1$$−ϕ$$2R$$⇒ϕ$$2=$$ϕ$$1$$−QR⇒$$6$$×$$10$$−$$3$$×$$cos$$θ$$=6$$×$$10$$−$$3$$−$$3$$×$$10$$−$$4$$×$$10$$⇒$$cos$$θ$$=3$$×$$10$$−$$36$$×$$10$$−$$3$$⇒θ$$=60o$$

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