A circular coil having N turns and radius r carries a current I. It is held in the XZ plane in a magnetic field B hati . The torque on the coil due to the magnetic field is :

Question

A circular coil having N turns and radius r carries a current I. It is held in the XZ plane in a magnetic field B hati . The torque on the coil due to the magnetic field is : (A) B π r2 IN (B)  (B r2 I/π N) (C) Zero (D)  (B π r2 I/N)

Tardigrade Admin · Accepted Answer

Magnetic moment of coil = NIA hatj = NI(π r2) hatj Torque on loop (coil) = vecM × vecB = NI (π r2) B sin 90° ( - hatk) = NI π r2 B ( - hatk )

Q. A circular coil having $N$ turns and radius $r$ carries a current $I$ . It is held in the $XZ$ plane in a magnetic field $B \hat{i}$ . The torque on the coil due to the magnetic field is :

$B π r^{2} I N$

$\frac{B r ^{2} I}{π N}$

Zero

$\frac{B π r ^{2} I}{N}$

Magnetic moment of coil = $N I A \hat{j}$
$= N I (π r^{2}) \hat{j}$
Torque on loop (coil) = $M \times B$
$= N I (π r^{2}) B sin 9 0^{\circ} (- \hat{k})$
$= N I π r^{2} B (- \hat{k})$

Q. A circular coil having N turns and radius r carries a current I. It is held in the XZ plane in a magnetic field Bi^ . The torque on the coil due to the magnetic field is :

Bπr2IN

πNBr2I​