Interaction Between Magnetic Dipoles
For separated small dipoles, dipole 1 produces B_1 proportional to m_1/r^3. Dipole 2 then has torque tau_2 = m_2 cross B_1 and force F = grad(m_2 dot B_1), giving F proportional to r^-4 for fixed orientations.
Why this shows up in the exam
Forces between small magnets · Torque on one dipole due to another · Fields at the midpoint of several magnets
Learn the idea
One dipole's non-uniform field exerts orientation-dependent force and torque on another dipole. Each magnet sits in the other magnet's field. The local field tries to turn it, while the spatial change of that field can pull or push it; because a dipole field falls as r cubed, the force falls as r to the fourth.
🧠 Memory hook: Dipole field is r⁻³; its pull adds one derivative, r⁻⁴.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- tau₂ = m₂ cross B₁ — torque on dipole 2 due to dipole 1
- F = grad(m₂ dot B₁) — dipole-dipole force in the field gradient
- B proportional to r⁻³; F proportional to r⁻⁴ — far-separation distance laws
How to approach it
- 1Find the first dipole's field at the second
- 2Resolve its direction before taking torque or energy
- 3Differentiate the r⁻³ energy dependence for force scaling
Common slip-ups that cost marks
- •Using an inverse-square force law
- •Ignoring vector orientation
- •Applying the point-dipole model when separation is comparable to magnet size
🌟 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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