Question

A 104 A current circulates around a 1.80-mm-diameter superconducting ring.

a)

What is the ring's magnetic dipole moment?

Express your answer with the appropriate units.

b)

What is the on-axis magnetic field strength 6.00 cm from the ring?

Express your answer with the appropriate units.

Answer 1

(a) The ring's magnetic dipole moment which will be given by -

= I A

where, I = current = 104 A

A = area of the loop = R²

then, we get

= [(104 A) (3.14) (0.9 x 10^-3 m)²]

= 0.000264 A.m²

= 2.64 x 10^-4 A.m²

(b) The on-axis magnetic field strength from the ring which will be given by -

B = (₀ / 4) (2 I A / z³)                                        { For z >> R }

B = [(4 x 10^-7 mT/A) (2) (2.64 x 10^-4 A.m²)] / [(4) (0.06 m)³]

B = [(5.28 x 10^-11 T.m³) / (0.000216 m³)]

B = 2.44 x 10^-7 T