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  4. 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 45° . 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 <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-zt4uu9t4sj44wpdb.jpg />

Q. Figure shows a closed loop of wire that consists of a pair of equal semicircles, of radius , 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 is directed perpendicular to the fold diameter and makes equal angles of with the planes of the semicircles, initially . The loop is rotated at a constant angular velocity 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 . The magnetic moment of the loop is

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Solution:

The flux of the magnetic field through the loop when it has rotated through , is


Current,
Magnetic moment current area

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