Electric-Dipole Potential
For r much larger than charge separation, an ideal dipole of moment p directed from negative to positive charge has potential k p dot rhat/r^2.
Why this shows up in the exam
axial and equatorial comparisons · far-field multipole scaling · combined dipoles and zero potential
Learn the idea
A short dipole has angular potential proportional to p cos(theta)/r squared. Far from two opposite charges, their leading 1/r potentials nearly cancel; the surviving directional term is strongest on the axis and zero on the equatorial plane.
🧠 Memory hook: Dipole potential remembers direction through cos theta.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- V = (1/(4 pi epsilon₀)) p cos(theta)/r² — ideal or far-field dipole, r much larger than separation
- p = q d — two equal opposite charges separated by vector d from negative to positive
How to approach it
- 1Confirm the far-field condition
- 2Mark theta from p to r
- 3Use cos theta and retain its sign
Common slip-ups that cost marks
- •Using the 1/r cubed field law for potential
- •Reversing the dipole-moment direction
- •Applying the approximation close to either charge
🌟 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.
More from Electrostatics
Electric dipoles and molecular dipole moments
Study the properties of electric dipoles, their fields and potentials, behavior in electric fields, and the distinction between polar and non-polar molecules.
Capacitors, capacitance, and combinations
Learn about parallel plate capacitors, series and parallel combinations, and how capacitance changes with geometry and dielectrics.
Energy stored in capacitors and conservation of charge
Examine how energy is stored, transferred, or lost in capacitors, including during charging, discharging, and redistribution, and the principle of charge conservation.
Gauss's law and its applications
Learn Gauss's law, electric flux, and how to use symmetry to find electric fields of charged spheres, shells, and other symmetric objects.
Coulomb's law and electric field of point charges
Understand Coulomb's law, the principle of superposition, and how to calculate the electric field due to point charges and simple charge distributions.
Conductors, charge distribution, and electrostatic shielding
Understand how charges distribute on conductors, the concept of electrostatic shielding, and the minimization of potential energy in conductors.