A circular insulated copper wire loop is twisted to form two loops of area A and $$2A$$ as shown in the figure. At the point of crossing the wires remain electrically insulated from each other. The entire loop lies in the plane (of$$ the $$paper). A uniform magnetic field B→ points into the plane of the paper. At $$t=0$$ , the loop starts rotating about the common diameter as axis with a constant angular velocity ω in the magnetic field. Which of the following options $$is/are$$ correct?

Question

A circular insulated copper wire loop is twisted to form two loops of area A and $$2A$$ as shown in the figure. At the point of crossing the wires remain electrically insulated from each other. The entire loop lies in the plane (of$$ the $$paper). A uniform magnetic field B→ points into the plane of the paper. At $$t=0$$ , the loop starts rotating about the common diameter as axis with a constant angular velocity ω in the magnetic field. Which of the following options $$is/are$$ correct?

Infinity Learn · Accepted Answer

emf induced in the loop  $$1=ddtBAcos$$ωtemf induced in the loop  $$2=ddtB2Acos$$ωtBut these two are in opposite sense , as Area vectors are in opposite direction.$$Enet=E2$$−$$E1=$$−$$ddtB2Acos$$ωt−−ddtBAcosωt​⇒$$Enet=B2Asin$$ωt−BAsinωt​⇒$$Enet=Bsin$$ωt $$2A$$−A⇒ Net emf induced ∝  difference of area,  so option  A is wrongRate of change of flux ddtBAcosωt or  $$ddtB2Acos$$ωt will be max when ω$$t=90$$° so option B is correct.$$Enet=E1$$ so option D is correct

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