Question

A current carrying loop is placed in a uniform magnetic field. The torque acting on the loop does not depend upon

• A. area of loop
• B. number of turns in the loop
• C. shape of the loop
• D. strength of the magnetic field

Hint:

The torque formula can be compactly written in terms of the magnetic dipole moment as $\vec{\tau} = \vec{M} \times \vec{B}$, where $M = NIA$. Because the magnetic dipole moment depends exclusively on the aggregate area enclosed and not on the geometry of the perimeter wire, shape is completely irrelevant.

Answer 1

The Correct Option is C

Step 1: Write the torque law and read off its variables.
The torque on a current loop is $\tau = N I A B \sin\theta$. Whatever symbol appears here is a genuine dependence; whatever is absent is not.
Step 2: Check the number of turns.
$N$ appears explicitly, so torque does depend on the number of turns.
Step 3: Check the area.
$A$ appears explicitly, so torque depends on the enclosed area.
Step 4: Check the field strength.
$B$ appears explicitly, so torque depends on the magnetic field strength.
Step 5: Look for shape.
Only the enclosed area $A$ enters, not the outline; two loops with equal area, current and turns give equal torque whether circular, square or triangular.
Step 6: Conclude.
Torque is independent of the loop's shape. \[ \boxed{\text{Independent of the shape of the loop}} \]