The magnetic field at the centre of a current carrying circular coil of area ' A ' is ' B '. The magnetic moment ( M ) of the coil is ( ₀= permeability of free space)

Step-by-step solution

The magnetic field at the center of a single-turn circular coil of area A carrying current I is B = ₀ I 2R , where the radius R = A . The magnetic moment is M = IA , so I = M A . Substituting both expressions into the magnetic field equation yields: B = ₀ ( M A ) 2 A which simplifies to B = ₀ M 2 A^ 3/2 . Solving for the magnetic moment gives: M = 2 B A^ 3/2 ₀ This expression corresponds to option B .