JEE Main · 2019 · 08 Apr 2019 · Shift 1 · Magnetic Effects of Current

A circular coil having

N

turns and radius

r

carries a current. It is held in the

X Z

plane in a magnetic field

B \hat{i}

. The torque on the coil due to the magnetic field is:

(A) $\frac{Br ^{2} 1}{π N}$
(B)zero
(C) $\frac{B π r ^{2} 1}{N}$
(D) $B π r^{2} I N$ ✓ Correct

Answer: (D)

Solution

A circular coil lying in the XZ plane has its area vector, and hence its magnetic moment

M = N I (π r^{2})

, directed along the y-axis, perpendicular to that plane. The field is

B \hat{i}

, so moment and field are at right angles and the torque is a maximum,

τ = ∣ M \times B ∣ = N I π r^{2} B

, which in the notation of the choices is

B π r^{2} I N

JEE Main · 2019 · 08 Apr 2019 · Shift 1 · Single correct option

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