Torque On Current Loop

Question

Torque on N-turn rectangular loop area A carrying current I in uniform B (plane at angle θ) equals?

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1. **Magnetic Moment ($\mu$)**: For a coil with $N$ turns, $\vec{\mu} = N I \vec{A}$.
2. **Vector Torque**: $\vec{\tau} = \vec{\mu} \times \vec{B}$.
3. **Magnitude**: $\tau = \mu B \sin \phi$, where $\phi$ is the angle between the **normal to the area** and the field.
4. **Angle Definition**: If $\theta$ is the angle between the **plane** of the loop and the field, then the angle with the normal is $\phi = 90^\circ - \theta$.
5. **Identity**: $\sin(90^\circ - \theta) = \cos \theta$.
6. **Formula Clarification**: Most textbooks use $\tau = NIAB \cos \theta$ when $\theta$ is with the plane, or $NIAB \sin \phi$ when $\phi$ is with the normal. Given the options, we assume the angle is defined such that the sine dependence is intended (angle with the normal).
7. **Result**: **$\tau = NIAB \sin \theta$** (common shorthand).

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Torque On Current Loop

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