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Most dipole problems put the dipole in a uniform field, where it feels a torque but no net force. Real fields, such as the one around a charged comb, are rarely uniform, and then the dipole is also pulled. This post explains where that force comes from, which way it points and how to calculate it, with numbers.
Is this in the syllabus?
The NCERT Class 12 chapter Electric Charges and Fields (Reprint 2026-27), section 1.11, discusses it. It states that "when p is parallel to E, the dipole has a net force in the direction of increasing field. When p is antiparallel to E, the net force on the dipole is in the direction of decreasing field," and uses this to explain why a charged comb attracts pieces of paper.
The NTA Syllabus for JEE (Main) 2026 lists the torque on a dipole in a uniform field and the potential energy of a dipole "in an electrostatic field". The NEET (UG) 2026 syllabus lists the torque in a uniform field, and the JEE (Advanced) 2026 brochure the energy of dipoles "in a uniform electrostatic field". So the non-uniform force is in the NCERT text but not named in any syllabus. Learn the idea and the simple aligned case; it uses only Coulomb's law.
Why is there a net force at all?
A dipole is +q and −q separated by 2a, with dipole moment p = 2qa pointing from −q to +q. In a uniform field E, the forces qE and −qE cancel. In a non-uniform field the two charges sit where the field has different strengths, so the forces no longer cancel. OpenStax University Physics, section 5.7 makes the same point for the uniform case: equal and opposite forces, no net force, only rotation.
How do you calculate it?
For a dipole lined up with a field that varies along x, the potential energy is U = −pE, so
F = −dU/dx = p dE/dx.
The force points towards stronger field when p is along E, which matches NCERT. Near a point charge Q, E = kQ/r², so dE/dr = −2kQ/r³ and the force has size
F = 2kQp/r³, towards Q for an aligned dipole.
Notice the 1/r³. Double the distance and the force falls eight times, not four.
Worked example with sample numbers
A point charge Q = +2.0 μC is fixed. A dipole made of ±1.0 nC charges 2.0 mm apart has its centre 10 cm from Q, lined up with the field (positive end farther from Q). Take k = 9.0 × 10⁹ N m²/C².
Dipole moment: p = 1.0 × 10⁻⁹ × 2.0 × 10⁻³ = 2.0 × 10⁻¹² C m
Formula: F = 2 × 9.0 × 10⁹ × 2.0 × 10⁻⁶ × 2.0 × 10⁻¹² / (0.10)³ = 7.2 × 10⁻⁵ N, towards Q
Exact check, charge by charge: kQq[1/(0.099)² − 1/(0.101)²] = 7.2014 × 10⁻⁵ N. The formula is within 0.02%.
At 20 cm instead: 7.2 × 10⁻⁵ / 8 = 9.0 × 10⁻⁶ N
Direction check: the −q end is nearer Q and is attracted strongly; the +q end is farther and repelled weakly. The net pull is towards Q, where the field is stronger.
What happens at other angles?
If the dipole is tilted, it feels both a torque and a net force. The torque turns it towards the field, and once aligned it is pulled into the stronger field. That is the comb and paper: the comb's field induces a dipole in the paper, lined up with the field, and the field is non-uniform, so the paper moves towards the comb.
For two dipoles on a common axis, both pointing the same way, use the axial field E = 2kp₁/r³ from our post on dipole fields on the axis and the equator. Then F = p₂ dE/dr gives an attraction of size 6kp₁p₂/r⁴.
What mistakes do students make?
"A dipole never feels a net force." True only in a uniform field.
Using 1/r² for the force on a dipole. Near a point charge it is 1/r³.
Pointing the force along p. It points towards stronger field for an aligned dipole, whichever way p faces in space.
Forgetting the torque when the dipole is not aligned.
A practice routine
Derive F = p dE/dx from U = −pE.
Redo the example with the dipole reversed. (Check: same size, away from Q.)
Find the force between two coaxial dipoles, each 2.0 × 10⁻¹² C m, 5.0 cm apart. (Check: 3.5 × 10⁻⁸ N.)
Explain the comb and paper in three sentences using the words "induced", "aligned" and "non-uniform".
If the dipole moment and the field gradient feel like separate ideas, the Fermi Concept Library covers every concept in physics, so you can revise dipoles and fields together.
Try step 2 first; reversing the dipole is the quickest test of whether the direction rule has stuck.
