Torque on a Current Loop
A planar N-turn loop has moment m = NIA n_hat and torque tau = m cross B. The magnitude is mB sin theta, where theta is between the loop normal and B.
Why this shows up in the exam
Torque on rectangular and circular coils · Finding loop orientation · Magnetic actuator and motor reasoning
Learn the idea
A uniform magnetic field turns a current loop to align its magnetic moment with the field. Opposite sides of the loop feel equal and opposite forces. They cancel as a net push but form a couple that rotates the loop.
🧠 Memory hook: Use the loop normal, not the loop plane, in the torque angle.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- m = N I A n_hat — magnetic moment of a planar N-turn loop
- tau = m cross B — torque vector in a uniform field
- |tau| = N I A B sin(theta) — torque magnitude
How to approach it
- 1Find area and moment direction
- 2Measure theta between m and B
- 3Use mB sin theta and the cross product for direction
Common slip-ups that cost marks
- •Measuring theta from the plane
- •Forgetting number of turns
- •Assigning a net translational force in a uniform field
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A charge of 2 microC moves perpendicular to a 3 T magnetic field at 4 x 10^5 m/s. Find the magnetic force.
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