Figure shows a closed loop of wire that consists of a pair of equal semicircles, of radius R, lying in mutually perpendicular planes. The loop was formed by folding a flat circular loop along a diameter until the two halves became perpendicular to each other. A uniform magnetic field of magnitude B is directed perpendicular to the fold diameter and makes equal angles (of$$ $$450) with the planes of the semicircles, initially (t$$ $$=$$ $$0). The loop is rotated at a constant angular velocity ω about the fold diameter. This induces an emf, which causes a current to flow in the wire. The resistance per unit length of the wire is λ. The magnetic moment of the loop is

Question

Figure shows a closed loop of wire that consists of a pair of equal semicircles, of radius R, lying in mutually perpendicular planes. The loop was formed by folding a flat circular loop along a diameter until the two halves became perpendicular to each other. A uniform magnetic field of magnitude B is directed perpendicular to the fold diameter and makes equal angles (of$$ $$450) with the planes of the semicircles, initially (t$$ $$=$$ $$0). The loop is rotated at a constant angular velocity ω about the fold diameter. This induces an emf, which causes a current to flow in the wire. The resistance per unit length of the wire is λ. The magnetic moment of the loop is

Infinity Learn · Accepted Answer

The flux of the magnetic field through the loop when it has rotated throughθ$$=$$ωt, is Φ$$=B$$$$π$$$$R222cos45$$∘$$cos$$ω$$tEMF=$$−dΦ$$dt=B$$$$π$$$$R2$$ω$$2sin$$ωt Current, $$i=EMF$$λ$$.2$$$$π$$RMagnetic moment $$=$$ current × $$area=B$$$$π$$$$R3$$ω$$4$$λ$$sin$$ωt

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