Electric Field of an Ideal Dipole
For r much greater than dipole size, E = [3(p dot r_hat)r_hat-p]/(4 pi epsilon_0 r^3). Axial and equatorial forms follow from this expression.
Why this shows up in the exam
Axial and equatorial field comparisons · Vector-direction questions · Far-field force scaling
Learn the idea
A far dipole field falls as 1/r³ and depends strongly on observation direction. On the axis the field is twice the equatorial magnitude; on the equatorial line it points opposite p. The vector formula handles arbitrary directions.
🧠 Memory hook: Axis gives two along p; equator gives one against p.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- E = k[3(p dot r_hat)r_hat - p]/r³ — far-field vector form
- E_axial = 2kp/r³ — magnitude on the dipole axis
- E_equatorial = kp/r³ — magnitude on the equatorial line, opposite p
How to approach it
- 1Test whether r is much larger than separation
- 2Identify axis, equator, or general angle
- 3Apply the vector direction before taking magnitude
Common slip-ups that cost marks
- •Using 1/r² for an ideal dipole
- •Missing the opposite direction on the equator
- •Using the far-field form near the charges
🌟 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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