Torque on a Loop of Current

When a current carrying wire is place in a magnetic field, it experiences a magnetic force. We can use the formula for Torque to calculate the total torque on a loop of current.

Definition §

Given a loop of wire with Current flowing through it, we can calculate the torque experienced when the loop is place in an external magnetic field.

Formula §

Torque on a Loop of Current in a Magnetic Field

$$\vec{\tau }={\vec{\mu }}_B\times \vec{B}=I\vec{A}\times \vec{B}$$

$$\vec{\tau }=IAB\sin (\theta )$$

Terms §

• $\vec{\tau }$ = Net Torque on loop (in $\text{Nm}$)
• ${\vec{\mu }}_B$ = Magnetic Dipole Moment (in ${\text{Am}}^2$)
• $\vec{B}$ = Magnetic Field (in $\text{T}$)
• $I$ = Current (in $\text{A}$)
• $\vec{A}$ = Area Vector (in ${\text{m}}^2$)
• $\theta$ = Angle between $\vec{A}$ and $\vec{B}$

This principle is used extensively in Motors. The direction of the torque is the axis on which the motor spins on. A higher torque means higher angular acceleration, i.e. faster spin.

In a motor §

A motor consists of a square loop of current in a uniform magnetic field perpendicular to it’s base:

https://www.youtube.com/watch?v=4FHQK3KcYqY