Dipole in a Non-Uniform Field: Net Force and Motion

Physics · Electric Charges And Fields · NEET

In a uniform field the two charges of a dipole feel equal and opposite forces, so the net force is zero (only torque acts). In a NON-uniform field the two ends sit where the field strength differs, so the forces no longer cancel and a net force appears. That net force pulls the dipole toward the region of STRONGER field, because moving there lowers its energy U = -pE. Memory hook: "uneven field = uneven forces = a real pull; the dipole chases the strong side."
Dipole in a Non-Uniform Field (weak left, strong right)weaker Estronger E-q+qpqE (small)qE (big)forces unequal -> net force to the RIGHTnet FU = -pE drops
The field lines get denser toward the right (stronger E). The +q end sits in the stronger field, so its force qE is bigger than the force on the -q end. The two forces no longer cancel, giving a net force toward the stronger-field side, where U = -pE is lowest.

Your doubts, answered

Why is the net force zero in a uniform field but non-zero in a non-uniform field?

In a uniform field E is the same everywhere. The +q end feels +qE and the -q end feels -qE. These are equal in size and opposite in direction, so they cancel: net force = 0 (only a turning torque is left). In a non-uniform field E is bigger at one end than the other. Now +qE and -qE have different sizes, so they do NOT cancel, and a net translational force is left over.

In which direction does the dipole move?

Once the dipole aligns with the field (torque does this first), it moves toward the region where the field is STRONGER. Reason: the potential energy is U = -p·E = -pE (when aligned). The field E is larger in the strong region, so U becomes more negative there. Nature always moves to lower energy, so the dipole is pulled into the stronger-field region.

Does the dipole feel only force, or force and torque together?

In general it feels BOTH. The torque tries to align p with E, and the net force tries to drag it toward the strong-field side. NCERT simplifies to two easy cases: when p is exactly parallel or antiparallel to E, the torque is zero, so ONLY a net force remains. This is the case NEET usually pictures.

Why does a charged comb pick up small pieces of paper?

This is the classic NCERT example. The comb's field is non-uniform (stronger near the comb). It induces a dipole in each paper bit (polarisation), with p pointing along the field. Because the field is non-uniform, this induced dipole feels a net force toward the comb (the stronger-field side), so the paper jumps to the comb.

If p is antiparallel to E, does the dipole still get pulled to the strong side?

No. If p points opposite to E, then U = -pE cos180 = +pE, which is HIGHER where the field is stronger. So an antiparallel dipole is pushed toward the WEAKER field. But a free dipole will first rotate (torque) to align p with E, and then it gets pulled to the stronger side. Watch the alignment before deciding the direction.

⚠️ The NEET trap
Choosing 'the dipole moves toward the weaker field' or 'no net force acts, only torque'.
An aligned dipole (p parallel to E) moves toward the STRONGER field because U = -pE drops there. A net force exists only because the field is non-uniform; torque may act too.
🧠 Uniform field -> torque only. Non-uniform field -> torque PLUS a net pull toward the strong side (lower U).

Real NEET questions

NEET 2021

A dipole is placed in a non-uniform electric field as shown, with the field stronger toward the right. In which direction will it move?

A · towards the left as its potential energy will increase
B · towards the right as its potential energy will increase
C · towards the left as its potential energy will decrease
D · towards the right as its potential energy will decrease
Solution: Step 1: In a non-uniform field the two charges feel unequal forces, so there is a NET force (not just torque). Step 2: The dipole aligns with E, then its energy is U = -p.E = -pE. Step 3: E is larger on the stronger-field side (right). So U becomes more negative (decreases) as the dipole moves right. Step 4: Systems move toward lower potential energy, so the dipole moves toward the right as U decreases. Answer: (D).

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Frequently asked

Does a dipole in a uniform field ever move?

It can rotate because of torque, but its centre does not get a net push (net force = 0). Only a non-uniform field gives a net translational force.

What is the formula for the net force on a dipole?

For a dipole aligned along x, the net force magnitude is F = p (dE/dx), the dipole moment times the rate at which the field changes with position. A larger gradient means a larger force. In a uniform field dE/dx = 0, so F = 0.

Why does the dipole go to the stronger field and not the weaker one?

Because its energy U = -pE is lowest where E is largest (once aligned). Objects settle into lower energy, so it is pulled to the strong-field region.

Is this the same idea as a paramagnetic material in a magnetic field?

Yes, it is the exact analogy. A paramagnetic (aligned) dipole moves from weak to strong field, just like this electric dipole. A diamagnetic (anti-aligned) one moves the opposite way.

Is this concept important for NEET?

Yes. NEET has directly asked which way a dipole moves in a non-uniform field (2021) and often combines it with U = -pE reasoning, so knowing the direction rule saves time.