Dipole Energy, Torque, and Rotation Work
For an ideal electric dipole in a uniform external field, torque is p cross E and orientation energy is -p dot E; quasistatic external work equals the energy change.
Why this shows up in the exam
180-degree dipole rotation · stable and unstable alignment · dipoles between capacitor plates
Learn the idea
A dipole tends to align with a uniform field because U=-p dot E. The field pulls opposite charges in opposite directions, making a turning effect. Parallel is minimum energy; antiparallel is maximum energy.
🧠 Memory hook: Parallel low, antiparallel high.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- U = -pE cos(theta) — uniform external field
- tau = pE sin(theta) — torque magnitude
- W_external = pE(cos theta_i - cos theta_f) — quasistatic rotation
How to approach it
- 1Draw p and E
- 2Write initial and final cosines
- 3Choose field or external work sign
Common slip-ups that cost marks
- •Using qV for the whole neutral dipole without both charges
- •Confusing field work with external work
- •Taking theta from the wrong direction
🌟 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.
Two point charges 1 microC and 2 microC are 1 m apart in vacuum. Take k = 9 x 10^9 SI. Find the force magnitude.
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