Question

A circular coil of 300 turns and a diameter 14cm carries a current of 15A. The value of magnetic moment ($in JT^{-1}$) associated with the loop is going to be:
A. 51.7
B. 69.3
C. 38.6
D. 19.5

Answer 1

In mechanics, the moment has several meanings like a moment of inertia, a moment of force, etc. But the word moment is used only where some rotation is observed. Here magnetic moment basically means the interaction of the magnetic field with the loop so as to observe a torque. Hence we can say that the magnetic moment is the measure of interaction between the loop and the magnetic field. The magnetic moment is denoted by “M”.
Formula used: M = NIA, where N is the number of turns, ‘I’ is the current passing through the loop and ‘A’ is the area of cross-section of the loop.

Complete step-by-step solution:
Given;
Number of turns (N) = 300
Current flowing (I) = 15A
Diameter = 14 cm
Radius = 7 cm = 0.07 m
Hence, area (A) = $\pi r^2 = \pi (0.07)^2= 0.01538 m^2$
Now, M = NIA
Putting the values;
$M = 300 \times 15 \times 0.01538 = 69.3 JT^{-1}$
Hence option B. is correct.

Additional information: In many cases, a loop can be treated as a bar magnet, especially when the point where the effect of the magnetic field is to be calculated is far from the loop.

Note: It seems that only material producing magnetic fields can only interact with the magnetic field. But it is not actually true. As we know that the charge at rest produces an only electric field, a charge moving with constant velocity produces electric and magnetic fields, and accelerated charge produces electric and magnetic fields, along with the generation of electromagnetic waves. Hence in the case of a current-carrying loop, the current means the flowing charges. Hence these moving charges produce a magnetic field which can easily interact with the external magnetic field and to measure this interaction, we use the concept of the magnetic moment