Two concentric, circular wire loops of radii r 1 = 23.8 cm and r 2 = 46.3 cm, ar

Question

Two concentric, circular wire loops of radii r1 = 23.8 cm and r2 = 46.3 cm, are located in an xy plane; each carries a clockwise current of 10.3 A (see the figure below). (a)Find the magnitude of the net magnetic dipole moment of the system. (b) Repeat for reversed current in the inner loop.

Two concentric, circular wire loops of radii r1 = 23.8 cm and r2 = 46.3 cm, are located in an xy plane; each carries a clockwise current of 10.3 A (see the figure below). (a)Find the magnitude of the net magnetic dipole moment of the system. (b) Repeat for reversed current in the inner loop.

Explanation / Answer

Magnetic dipole moment due to a current carrying coil is given by

M= I A

M= magnetic dipole moment, I= Current , A= area of circular loop = Pie * R^2. Pie= 3.14.

magnetic dipole moment due to both of the loops :

M (net) =( I *3.14*R1^2 )+( I * 3.14*R2^2)

=3.14*I* (R1^2+ R2^2)

=3.14*10.3*[(0.238)^2+(0.463)^2]

=3.14*10.3*(0.0566+0.2143)

=8.76 A-m^2 into page ie in inward direction according to right hand screw rule.

(b) When the current in the inner loop reversed, dipole will point in reversed direction

M(net)= I *3.14* (R2^2- R1^2)

=10.3*3.14*(0.2143-0.0566)

=5.1 A-m^2 into page

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