A circular loop of wire of radius 0.50 m is in a uniform magnetic field of 0.30 T. The current in the loop is 2.0 A. What is the magnetic torque when the plane of the loop is parallel to the magnetic field?

The magnetic torque when the plane of the loop is parallel to the magnetic field is zero.

Explanation:

Given;

radius of wire, r = 0.50 m

strength of magnetic field, B = 0.3 T

current in the wire, I = 2.0 A

Dipole moment, μ = I x A

where;

A is the area of the circular loop = πr² = π (0.5) ² = 0.7855 m²

Dipole moment, μ = 2A x 0.7855m² = 1.571 Am²

magnetic torque, τ = μBsinθ

when the plane of the loop is parallel to the magnetic field, θ = 0

τ = 1.571 Am² x 0.3sin0

τ = 0

Therefore, the magnetic torque when the plane of the loop is parallel to the magnetic field is zero.

Torque = 0.47 Nm

Explanation:

Torque = BIAsin∅

Since the plane is parallel to the magnetic field, ∅ = 90⁰

sin 90 = 1

Magnetic field, B = 0.30 T

current, I = 2.0 A

Radius, R = 0.50 m

A = πR²

A = π (0.5) ² = 0.785 m²

Torque = 0.3 * 2 * 0.785

Torque = 0.47 Nm