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: Understanding the Question:
The problem asks us to identify which of the given parameters does not affect the magnitude of the mechanical torque experienced by a current-carrying loop suspended within a uniform magnetic field.

Step 2: Key Formula or Approach:
The torque $\tau$ exerted on a planar current loop containing $N$ turns, bounding an internal area $A$, carrying a current $I$, inside a uniform magnetic field $B$ is expressed as:
$$\tau = NIAB \sin\theta$$ where $\theta$ is the angle between the magnetic field vector and the area vector (normal to the loop plane).

Step 3: Detailed Explanation:
Let's analyze each of the variables present in our torque formulation:
1. $\tau$ depends directly on the loop's enclosed surface Area ($A$), as given in option (A).
2. $\tau$ depends directly on the number of wire loops/turns ($N$), as given in option (B).
3. $\tau$ depends directly on the magnetic field induction strength ($B$), as given in option (D).
The geometric path outline or "shape" of the perimeter (whether it is a circle, rectangle, triangle, or an irregular closed curve) does not feature anywhere in the equation. As long as two loops share an identical total surface area $A$, number of turns $N$, and current $I$, they will experience the exact same torque under identical conditions regardless of shape.

Step 4: Final Answer:
The torque does not depend on the shape of the loop, which corresponds to option (C).