28.10:
Torque On A Current Loop In A Magnetic Field
Consider a rectangular current-carrying loop of lengths a and b placed in a uniform magnetic field, with an axis of rotation passing through point O at distance m from one end.
The magnetic forces acting along the plane of the loop lie on the same axis passing through O; thus, the sum of their torques about the axis is equal to zero.
Similarly, the torques due to the forces perpendicular to the plane of the loop can be determined.
By adding all the torques acting on the loop, the net torque can be determined, where A is the area of the loop.
A current-carrying closed loop can be referred to as a magnetic dipole. The magnetic dipole moment is a vector quantity, where the magnitude is the product of the area and the current flowing through the loop; its direction is perpendicular to the plane of the loop, following the right-hand rule.
Therefore, the torque on a current loop due to a uniform magnetic field can be described in terms of the magnetic dipole moment.
28.10:
Torque On A Current Loop In A Magnetic Field
The most common application of magnetic force on current-carrying wires is in electric motors. These consist of loops of wire, which are placed between the magnets with a magnetic field. When current flows through the loops, the magnetic field applies torque, which causes the shaft to rotate, thus converting electrical energy to mechanical energy.
Consider a rectangular current-carrying loop containing N turns of wire, placed in a uniform magnetic field. The net force on a current-carrying loop in a uniform magnetic field is zero, whereas the net torque can be defined as:
where I is the current flowing in the loop, A is the area of the loop, and θ is the angle between the current and the magnetic field. The maximum torque occurs when the current in the loop is perpendicular to the magnetic field, indicating θ = 90°, whereas the minimum torque occurs when θ is zero.
Consider a 200-turn square loop of a wire with an area of 0.04m2, carrying 15 A of current in a 1-T field. Determine the maximum torque on the loop.
First, identify the known and unknown quantities. The maximum torque on the current-carrying loop is obtained when θ = 90° and sin θ = 1. Then, substitute the known values in the net torque equation:
Simplify the equation, to determine the maximum torque on the current-carrying loop.
A current-carrying closed loop can be referred to as a magnetic dipole. The loop's magnetic dipole moment is a vector quantity whose magnitude is equal to the sum of its area and the current flowing through it, and whose direction is perpendicular to the loop's plane. Consequently, the torque on a current loop caused by a uniform magnetic field can be explained in terms of the magnetic dipole moment.
Suggested Reading
- OpenStax. (2019). University Physics Vol. 2. [Web version], Pg 396 – 398. Retrieved from https://openstax.org/books/university-physics-volume-2@8ede2ba/pages/11-4-magnetic-force-on-a-current-carrying-conductor