Magnetic Moment and Number of Turns – Rankers Physics
Topic: Magnetic Effects of Current
Subtopic: Bar Magnet

Magnetic Moment and Number of Turns

Assertion (A): To produce high magnetic moment from a current carrying cable, it should be turned in maximum number of circular loops.
Reason (R): Magnetic moment is directly proportional to number of turns of circular loop for a given length of wire.
 
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution:

Magnetic moment is \(M = NIA\). For a fixed wire length \(L\), \(r = L/(2\pi N)\) and \(A = \pi r^2 = L^2/(4\pi N^2)\). So \(M = IL^2/(4\pi N)\). Assertion (A) is false as \(M\) is inversely proportional to \(N\). Reason (R) is false as \(M\) is inversely proportional to \(N\) for a given wire length. Both (A) and (R) are false.

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