The figure shows a circular loop of radius $a$ with two long parallel wires (numbered 1 and 2) all in the plane of the paper. The distance of each wire from the centre of the loop is $d$. The loop and the wires are carrying the same current $I$. The current in the loop is in the counterclockwise direction if seen from above. Consider $d \gg a$, and the loop is rotated about its diameter parallel to the wires by 30° from the position shown in the figure. If the currents in the wires are in the opposite directions, the torque on the loop at its new position will be (assume that the net field due to the wires is constant over the loop)

(B) $\frac{\mu_{0} I^{2} a^{2}}{2d}$

(A) $\frac{\mu_{0} I^{2} a^{2}}{d}$

(C) $\frac{\sqrt{3} \mu_{0} I^{2} a^{2}}{d}$

(D) $\frac{\sqrt{3} \mu_{0} I^{2} a^{2}}{2d}$

JEE Advanced · 2014 · 25 May 2014 · Paper 2 · Magnetic Effects of Current

The figure shows a circular loop of radius

a

with two long parallel wires (numbered 1 and 2) all in the plane of the paper. The distance of each wire from the centre of the loop is

d

. The loop and the wires are carrying the same current

I

. The current in the loop is in the counterclockwise direction if seen from above.

Consider

d ≫ a

, and the loop is rotated about its diameter parallel to the wires by 30° from the position shown in the figure. If the currents in the wires are in the opposite directions, the torque on the loop at its new position will be (assume that the net field due to the wires is constant over the loop)

(A) $\frac{μ _{0} I ^{2} a ^{2}}{d}$
(B) $\frac{μ _{0} I ^{2} a ^{2}}{2 d}$ ✓ Correct
(C) $\frac{3 μ _{0} I ^{2} a ^{2}}{d}$
(D) $\frac{3 μ _{0} I ^{2} a ^{2}}{2 d}$

Answer: (B)

Solution

When the two wires carry currents in opposite directions, the net magnetic field at the loop's center is

B = 2 \times \frac{μ _{0} I}{2 π d} = \frac{μ _{0} I}{π d}

.

The magnetic moment of the loop is

M = I π a^{2}

.

When rotated by 30°, the torque is

τ = M B sin (30°) = I π a^{2} \times \frac{μ _{0} I}{π d} \times \frac{1}{2} = \frac{μ _{0} I ^{2} a ^{2}}{2 d}

JEE Advanced · 2014 · 25 May 2014 · Paper 2 · Single correct option

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JEE Advanced · 2014 · 25 May 2014 · Paper 2 · Magnetic Effects of Current

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