Current i is carried in a wire of length L. If the wire is...

Current $i$ is carried in a wire of length $L$. If the wire is turned into a circular coil, the maximum magnitude of torque in a given magnetic field $B$ will be
(A) $\frac{L^{2} i B}{2}$
(B) $\frac{L^{2} i B}{\pi}$
(C) $\frac{L^{2} i B}{4 \pi}$
(D) $\frac{L i^{2} B}{4 \pi}$

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Key Concepts

Geometric Relationship Between Wire Length and Circular Area

When a straight wire is reshaped to form a circular coil, its length becomes the circumference of the circle. Knowing the circumference allows us to determine the radius and subsequently calculate the area of the circle. This conversion is essential in problems where the area of the loop is needed to find the magnetic dipole moment.

Torque on a Current Loop in a Magnetic Field

A current loop placed in a magnetic field experiences a torque, which tends to align the loop’s magnetic dipole moment with the magnetic field. The maximum torque occurs when the dipole moment is perpendicular to the magnetic field. The expression for this torque is given by the product of the dipole moment and the magnetic field strength.

Magnetic Dipole Moment

The magnetic dipole moment is a measure of the strength and orientation of a current loop’s magnetic field. It is defined as the product of the current flowing through the loop and the area enclosed by the loop. This quantity plays a central role in determining how the loop interacts with external magnetic fields.

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