A current carrying circular loop of radius 2 cm with unit normal $\hat{n}=\frac{\hat{k}+\hat{i}}{\sqrt{2}}$ is placed in a magnetic field, $\overrightarrow{\mathrm{B}}=\mathrm{B}_{0}(3 \hat{\mathrm{i}}+2 \hat{\mathrm{k}})$. If $\mathrm{B}_{0}=4 \times 10^{-3} \mathrm{~T}$ and current $\mathrm{I}=100 \sqrt{2} \mathrm{~A}$, the torque experienced by the loop is ______ Wb.A. $(\pi=3.14)$

(D) $5024 \times 10^{-7} \hat{\mathrm{j}}$

(A) $16 \times 10^{-5} \hat{\mathrm{k}}$

(B) $5024 \times 10^{-7} \hat{\mathrm{k}}$

(C) $5024 \times 10^{-7} \hat{\mathrm{i}}$

JEE Main · 2026 · 08 Apr 2026 · Shift 2 · Magnetic Effects of Current

A current carrying circular loop of radius 2 cm with unit normal

\overset{n}{^} = \frac{k ^ + i ^}{2}

is placed in a magnetic field,

B = B_{0} (3 \hat{i} + 2 \hat{k})

. If

B_{0} = 4 \times 1 0^{- 3} T

and current

I = 1002 A

, the torque experienced by the loop is ______ Wb.A.

(π = 3.14)

Answer: (D)

The magnetic moment is

M = I A \overset{n}{^} = 1002 \times π (0.02)^{2} \times \frac{i ^ + k ^}{2} = 100 π (0.02)^{2} (\hat{i} + \hat{k})

. The torque is

τ = M \times B

with

B = B_{0} (3 \hat{i} + 2 \hat{k})

. Since

(\hat{i} + \hat{k}) \times (3 \hat{i} + 2 \hat{k}) = 2 (\hat{i} \times \hat{k}) + 3 (\hat{k} \times \hat{i}) = - 2 \hat{j} + 3 \hat{j} = \hat{j}

τ = 100 π (0.02)^{2} B_{0} \hat{j} = 100 \times 3.14 \times 4 \times 1 0^{- 4} \times 4 \times 1 0^{- 3} \hat{j} = 5024 \times 1 0^{- 7} \hat{j}

. The torque experienced by the loop is

5024 \times 1 0^{- 7} \hat{j}

JEE Main · 2026 · 08 Apr 2026 · Shift 2 · Single correct option