Magnetic Dipole Equivalence of Circular Coil – Rankers Physics
Topic: Magnetic Effects of Current
Subtopic: Bar Magnet

Magnetic Dipole Equivalence of Circular Coil

Assertion (A): A planar circular coil of area \(A\) and current \(I\) is equivalent to magnetic dipole of dipole moment \(M = IA\).
Reason (R): At large distances, magnetic field of circular loop and magnetic dipole is same.
 
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:

Assertion (A) is true. The magnetic dipole moment \(M\) of a current loop with area \(A\) and current \(I\) is indeed given by \(IA\). Reason (R) is also true. At large distances, the magnetic field produced by a circular current loop is identical to the field of an ideal magnetic dipole with moment \(IA\). Reason (R) provides the correct explanation for Assertion (A) as this equivalence is the basis for the definition of the magnetic dipole moment.

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