A circular loop with N turns has radius r . It lies in the x-y plane carrying current I in the anti-clockwise direction. If the magnetic field in the region is overset arrow B=B0 hati, then find the torque (. overset arrow τ.) acting on the loop.

Question

A circular loop with N turns has radius r . It lies in the x-y plane carrying current I in the anti-clockwise direction. If the magnetic field in the region is overset arrow B=B0 hati, then find the torque (. overset arrow τ.) acting on the loop. (A) B0 NI π r2 hatj (B) B0I π r2 hatj (C) B0 NI π r2 hatk (D) B0 π r2 hatk

Tardigrade Admin · Accepted Answer

Magnetic moment overset arrow M=NI(π r2) hatk Torque overset arrow τ= overset arrow M× overset arrow B =(N I (π r2) hatk)× (.B0 hati.) =B0NI π r2 hatj Nm

Q. A circular loop with $N$ turns has radius $r$ . It lies in the x-y plane carrying current $I$ in the anti-clockwise direction. If the magnetic field in the region is $B \to = B_{0} \hat{i},$ then find the torque $(τ \to)$ acting on the loop.

$B_{0} N I π r^{2} \hat{j}$

$B_{0} I π r^{2} \hat{j}$

$B_{0} N I π r^{2} \hat{k}$

$B_{0} π r^{2} \hat{k}$

Magnetic moment $M \to = N I (π r^{2}) \hat{k}$
Torque $τ \to = M \to \times B \to$
$= (N I (π r^{2}) \hat{k}) \times (B_{0} \hat{i})$
$= B_{0} N I π r^{2} \hat{j} N m$

Q. A circular loop with N turns has radius r . It lies in the x-y plane carrying current I in the anti-clockwise direction. If the magnetic field in the region is B→=B0​i^, then find the torque (τ→) acting on the loop.

B0​NIπr2j^​

B0​Iπr2j^​

B0​NIπr2k^

B0​πr2k^