JEE Main · 2020 · 05 Sep 2020 · Shift 1 · Magnetic Effects of Current

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A square loop of side 2a, and carrying current I , is kept in XZ plane with its centre at origin. A long wire carrying the same current I is placed parallel to the z -axis and passing through the point

(0, b, 0), (b ≫ a)

. The magnitude of the torque on the loop about z - axis is given by:

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

Answer: (D)

Solution

The long wire produces a field

B = \frac{μ _{0} I}{2 π b}

in the region of the loop. The two sides of the square that run parallel to the wire, each of length

2 a

, carry oppositely directed currents and so feel equal and opposite forces

F = B I (2 a) = \frac{μ _{0} I ^{2} a}{π b}

, forming a couple. Taking the moment of this couple about the

z

-axis with arm

a

, the torque is

τ = 2 F a = \frac{2 μ _{0} I ^{2} a ^{2}}{π b}

JEE Main · 2020 · 05 Sep 2020 · Shift 1 · Single correct option

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JEE Main · 2020 · 05 Sep 2020 · Shift 1 · Magnetic Effects of Current

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