Torque On Current Loop

Question

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

RankGuru · Accepted Answer

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).

Torque On Current Loop

Select the correct option:

🔒 Solution Hidden from View

More magnetic effects and magnetism Practice Questions

Ampere's law integral form states ∮ B·dl equals?

Energy density u of magnetic field B in vacuum is?

Horizontal component of Earth's field Bh relates to total B and dip angle δ by?

Differential magnetic field dB due to current element Idl at position vector r (angle θ)?

Magnetic field at distance r from long straight wire carrying current I?

Lorentz force vector expression?

Cyclotron angular frequency ω for charge q, mass m in magnetic field B?

Magnetic field inside long solenoid (turns per length n, current I) approximately?

Magnitude of magnetic force on charge q moving with velocity v perpendicular to uniform B?

Field at center of circular loop radius R carrying current I?

Magnetic moment of single current loop (current I, area A)?

Hysteresis loop area represents?

About This Question

Solution