Dipole-Dipole Interaction
For ideal dipoles separated by r, U = k[p_1 dot p_2 - 3(p_1 dot r_hat)(p_2 dot r_hat)]/r^3. Force follows from the spatial gradient of U.
Why this shows up in the exam
Fields of paired dipoles · Energy released as dipoles separate · Orientation-dependent attraction
Learn the idea
Each dipole feels the nonuniform field produced by the other, creating orientation-dependent force and energy. Two dipoles can attract or repel depending on how their moments face the separation direction. Their interaction changes as 1/r³ in energy and 1/r⁴ in force.
🧠 Memory hook: Dipole pairs care about both moment directions and the joining axis.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- U = k[p₁ dot p₂ - 3(p₁ dot r_hat)(p₂ dot r_hat)]/r³ — ideal dipole-dipole interaction energy
- F_r = -dU/dr — radial force for fixed orientations
How to approach it
- 1Draw p₁, p₂, and r_hat
- 2Evaluate the dot products
- 3Use energy conservation or differentiate only after fixing orientation
Common slip-ups that cost marks
- •Treating dipoles as point charges with 1/r² force
- •Ignoring relative orientation
- •Using the energy formula outside the far-separation limit
🌟 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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