Question

A uniform conducting wire of length $12\, a$ 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. $\sqrt{3} Ia ^{2}$ and $3\, Ia ^{2}$
• B. $3\, Ia ^{2}$ and $Ia ^{2}$
• C. $3\, Ia ^{2}$ and $4\, Ia ^{2}$
• D. $4\, Ia ^{2}$ and $3\, Ia ^{2}$

Answer 1

Answer: (A)

(i) If it is an equilateral triangle of side '$a$' no. of triangular loops formed $\frac{12 a}{3 a}=4$
and magnetic moment $4 \cdot \frac{\sqrt{3} a^{2}}{4} l=\sqrt{3} l a^{2}$
(ii) Side of the square if it is a.
No. of square formed $\frac{12 a}{4 a}=3$
Magnetic moment of the square loop is $3 a^{2} I$.