2021 Magnetism and MatterMagnetic Dipole Moment of a Current Loop Hard Question 11 of 38 in Magnetism and Matter

A uniform conducting wire of length $12a$ and resistance $R$ is wound up as a current carrying coil in the shape of, (i) an equilateral triangle of side $a$. (ii) a square of side $a$. The magnetic dipole moments of the coil in each case respectively are:

A $3Ia^2$ and $Ia^2$
B $3Ia^2$ and $4Ia^2$
C $4Ia^2$ and $3Ia^2$
D $\sqrt{3}Ia^2$ and $3Ia^2$

The answer is D.

Solution

Wire length = 12a. (i) Equilateral triangle of side a: perimeter 3a, so number of turns = 4. $M_1 = NIA = 4 \times I \times \frac{\sqrt{3}}{4}a^2 = \sqrt{3}Ia^2$ (ii) Square of side a: perimeter 4a, so number of turns = 3. $M_2 = 3 \times I \times a^2 = 3Ia^2$

Concept dipole moment of a wound coil

Magnetism and Matter in past papers

38 questions from this chapter have appeared across 21 exam years.