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:

Question

Aicharya · Accepted Answer

Area of equilateral triangle of side a,

$A = \frac{1}{2} \times a \times \frac{\sqrt{3} a}{2} = \frac{\sqrt{3}}{4} a^{2}$

Magnetic moment of each triangle,

$m = I A = \frac{\sqrt{3}}{4} a^{2} I$

$12 a$ length of wire will form $4$ loops of triangle of side $a$ .

Magnetic moment of triangle,

$M_{1} = N m = 4 \times \frac{\sqrt{3}}{4} a^{2} I = \sqrt{3} I a^{2}$

Similarly, magnetic moment of square

$M_{2} = N m = 3 \times (I a^{2})$

$= 3 I a^{2}$

A uniform conducting wire of length 12 a and resistance R is wound up as a current-carrying coil in the…

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