A uniform conducting wire of length length 10a and resistance R is wound up into four turn as a current carrying coil in the shape of equilateral triangle of side a. If current I is flowing through the coil then the magnetic moment of the coil is

Question

A uniform conducting wire of length length 10a and resistance R is wound up into four turn as a current carrying coil in the shape of equilateral triangle of side a. If current I is flowing through the coil then the magnetic moment of the coil is <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/b9535912cb3e9c279065d0eb0bf2134e-.jpeg" /> (A) (√3/2) a2I (B) (a2 I/√3) (C) √3a2I (D) (2a2I/√3)

Tardigrade Admin · Accepted Answer

Magnetic moment M=NIA =4× I× a2 (√3/4) =√3a2 I

Q. A uniform conducting wire of length length $10 a$ and resistance $R$ is wound up into four turn as a current carrying coil in the shape of equilateral triangle of side $a$ . If current $I$ is flowing through the coil then the magnetic moment of the coil is

$\frac{3}{2} a^{2} I$

$\frac{a ^{2} I}{3}$

$3 a^{2} I$

$\frac{2 a ^{2} I}{3}$

Magnetic moment $M = N I A$
$= 4 \times I \times a^{2} \frac{3}{4}$
$= 3 a^{2} I$

Q. A uniform conducting wire of length length 10a and resistance R is wound up into four turn as a current carrying coil in the shape of equilateral triangle of side a. If current I is flowing through the coil then the magnetic moment of the coil is

23​​a2I

3​a2I​

3​a2I

3​2a2I​