Question

A current of \(50\,mA\) flows through a loop of area \(10\,cm^{2}\) placed in a magnetic field of \(0.1\,T\). The angle between the magnetic field and the loop is \(60^{\circ}\). Find the torque acting on the loop.

• A. \(2.5\times10^{-5}\,Nm\)
• B. \(4.33\times10^{-5}\,Nm\)
• C. \(4.33\times10^{-6}\,Nm\)
• D. \(2.5\times10^{-6}\,Nm\)

Hint:

Always remember the torque on a current-carrying loop: \[ \boxed{\tau=NIAB\sin\theta} \] where \(\theta\) is the angle between the magnetic field and the normal to the plane of the loop. If the angle is given with the plane of the loop, first convert it using \[ \boxed{\theta=90^{\circ}-\phi.} \] This is one of the most common mistakes in magnetic torque problems.

Answer 1

The Correct Option is C

The magnetic dipole moment of a current loop is $m = IA$. Substituting $I = 50 \times 10^{-3}$ A and $A = 10 \times 10^{-4}$ m² gives $m = 5 \times 10^{-5}$ A·m².