Magnetic Potential Energy and Work
For a fixed dipole in a uniform field, U = -m dot B = -mB cos theta. Slow external work from theta_1 to theta_2 equals Delta U = mB(cos theta_1 - cos theta_2).
Why this shows up in the exam
Work needed to reverse a magnet or coil · Energy changes during rotation · Ranking orientations by stability
Learn the idea
A dipole has minimum energy parallel to a field and maximum energy antiparallel to it. A magnetic dipole naturally turns toward the field just as a ball moves toward lower gravitational energy. An external agent must supply energy to rotate it away from stable alignment.
🧠 Memory hook: Parallel is the energy valley; antiparallel is the hilltop.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- U = -m B cos(theta) — magnetic potential energy with zero chosen at 90 degrees
- W_external = Delta U — quasistatic work done by an external agent
- U_parallel = -mB; U_antiparallel = +mB — stable minimum and unstable maximum energies
How to approach it
- 1Write initial and final angles of m with B
- 2Evaluate U at both angles
- 3Use Delta U for slow external work and conserve energy for free rotation
Common slip-ups that cost marks
- •Using sin theta for potential energy
- •Forgetting that a full reversal changes energy by 2mB
- •Confusing work by the field with external work
🌟 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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