A square loop is carrying a steady current I and the magnitude of its magnetic dipole moment is m . If this square loop is changed to a circular loop and it carries the same current, the magnitude of the magnetic dipole moment of circular loop will be:

Question

A square loop is carrying a steady current I and the magnitude of its magnetic dipole moment is m . If this square loop is changed to a circular loop and it carries the same current, the magnitude of the magnetic dipole moment of circular loop will be:, 4 m π, 3 m π, 2 m π, m π

MARKS App · Accepted Answer

Let the side of square loop be a . The magnetic dipole is ∴ m = I a 2 a = m I Radius of circular loop r related to a as circumference of circular loop is equal to perimeter of square loop. 2 π r = 4 a = 4 m I r = 2 π m I ∴ New dipole moment m ' = π 2 π m I 2 I = 4 m π

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