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Electric Dipole in External Electric Field

An electric dipole consists of two equal and opposite charges separated by a small distance.

Let the charges be +q and -q.

Distance between the charges = 2a

Dipole moment:

p = q × 2a

Direction of dipole moment is from negative charge to positive charge.

When an electric dipole is placed in a uniform external electric field, two equal and opposite forces act on the two charges.

Force on +q:

F = qE

Force on -q:

F = qE

These two forces are equal in magnitude and opposite in direction. Therefore, net force on the dipole is zero.

Net force = 0

But these two forces form a couple. So the dipole experiences torque.

Diagram: Electric Dipole in Uniform Electric Field

Copy-paste friendly diagram:

Uniform Electric Field E →

        +q
        ●
        |\
        | \ 2a
        |  \
        |   \
        ●
        -q

Dipole moment p is from -q to +q.
Angle between p and E = θ

Torque Experienced by Dipole

Force on each charge:

F = qE

Perpendicular distance between the two forces:

d = 2a sin θ

Torque:

τ = Force × perpendicular distance

τ = qE × 2a sin θ

τ = q(2a)E sin θ

Since,

p = q(2a)

Therefore,

τ = pE sin θ

Vector form:

τ = p × E

Magnitude:

τ = pE sin θ

This torque tries to rotate the dipole and align it with the electric field.

Important Points

Net force on dipole in uniform electric field is zero.
Net torque on dipole is not zero if θ is not 0 degree or 180 degree.
Torque is maximum when θ = 90 degree.
Torque is zero when θ = 0 degree or θ = 180 degree.

Maximum torque:

τmax = pE

Minimum torque:

τ = 0

Potential Energy of Dipole in External Electric Field

Potential energy of an electric dipole in uniform electric field is:

U = -pE cos θ

Where:

U = potential energy
p = dipole moment
E = electric field
θ = angle between p and E

Stable Equilibrium

When dipole moment is in the same direction as electric field:

θ = 0 degree

U = -pE cos 0

cos 0 = 1

U = -pE

This is minimum potential energy. So this position is stable equilibrium.

Stable equilibrium:

θ = 0 degree

U = -pE

Unstable Equilibrium

When dipole moment is opposite to electric field:

θ = 180 degree

U = -pE cos 180

cos 180 = -1

U = +pE

This is maximum potential energy. So this position is unstable equilibrium.

Unstable equilibrium:

θ = 180 degree

U = +pE

Work Done in Rotating Dipole

Work done in rotating dipole from angle θ1 to θ2:

W = U2 – U1

Since,

U = -pE cos θ

So,

W = -pE cos θ2 – (-pE cos θ1)

W = pE(cos θ1 – cos θ2)

Work Done from Stable to Unstable Position

Stable position:

θ1 = 0 degree

U1 = -pE

Unstable position:

θ2 = 180 degree

U2 = +pE

Work done:

W = U2 – U1

W = pE – (-pE)

W = 2pE

So, work required to rotate dipole from stable to unstable position is:

W = 2pE

Work Done from Unstable to Stable Position

Unstable position:

U1 = +pE

Stable position:

U2 = -pE

Change in potential energy:

ΔU = U2 – U1

ΔU = -pE – pE

ΔU = -2pE

So, when dipole moves from unstable to stable position, potential energy decreases by:

2pE

This means energy is released, and the dipole naturally tends to align with the electric field.

Kumar Sir Style Explanation

Kumar Sir explains this topic in a very simple way:

If a dipole is placed in a uniform electric field, one charge feels force in one direction and the other charge feels force in the opposite direction. Since both forces are equal and opposite, net force becomes zero. But because the forces act at different points, they produce rotation. This rotation effect is called torque.

So remember:

Net force = 0

Torque = pE sin θ

Potential energy = -pE cos θ

Stable equilibrium means dipole is aligned with electric field.

Unstable equilibrium means dipole is opposite to electric field.

This is very important for NEET Physics, JEE Physics, CBSE Class 12 Physics, IB Physics and AP Physics.

15 Conceptual Questions with Answers on Electric Dipole

1. Why is the net force on an electric dipole zero in a uniform electric field?

Answer:
In a uniform electric field, force on +q is qE in the direction of field and force on -q is qE opposite to the field. Both forces are equal and opposite, so net force is zero.

2. If net force is zero, why does the dipole rotate?

Answer:
Because the two equal and opposite forces act at different points. They form a couple, which produces torque and rotates the dipole.

3. Why does a dipole try to align with the electric field?

Answer:
The torque on the dipole rotates it in such a way that its dipole moment becomes parallel to the electric field. This is the stable position.

4. When is torque maximum?

Answer:
Torque is maximum when angle between dipole moment and electric field is 90 degree.

τ = pE

5. When is torque zero?

Answer:
Torque is zero when angle is 0 degree or 180 degree.

At these positions, forces do not produce rotation.

6. What is stable equilibrium of dipole?

Answer:
When dipole moment is parallel to electric field, θ = 0 degree. Potential energy is minimum, so it is stable equilibrium.

U = -pE

7. What is unstable equilibrium of dipole?

Answer:
When dipole moment is opposite to electric field, θ = 180 degree. Potential energy is maximum, so it is unstable equilibrium.

U = +pE

8. Why is potential energy minimum at θ = 0 degree?

Answer:
At θ = 0 degree, dipole is naturally aligned with electric field. This is the most stable position, so potential energy is minimum.

9. Why is potential energy maximum at θ = 180 degree?

Answer:
At θ = 180 degree, dipole is opposite to electric field. It is unstable and needs maximum energy to stay there.

10. What happens when dipole moves from unstable to stable position?

Answer:
Potential energy decreases from +pE to -pE. Energy is released.

Decrease in energy = 2pE

11. Work required to rotate dipole from stable to unstable position?

Answer:
Stable position energy = -pE
Unstable position energy = +pE

Work required:

W = +pE – (-pE)

W = 2pE

12. What are torque and potential energy at θ = 90 degree?

Answer:
At θ = 90 degree:

Torque is maximum:

τ = pE

Potential energy is zero:

U = 0

13. Why is U = -pE cos θ negative?

Answer:
Negative sign shows that dipole has minimum energy when it aligns with electric field. Nature always tries to bring the system to minimum energy.

14. Can a dipole translate in a uniform electric field?

Answer:
No. In uniform electric field, net force is zero, so dipole does not translate. It only rotates.

15. Can a dipole experience force in non-uniform electric field?

Answer:
Yes. In non-uniform electric field, forces on +q and -q are unequal, so net force is not zero. Therefore, dipole can translate as well as rotate.

Why Learn This Topic from Kumar Sir?

Kumar Sir has 30+ years of teaching experience. He teaches Physics step by step with concept clarity, derivation, diagram, formula and numerical practice. Students from Nagpur can connect online from Shankar Nagar, Dharampeth, Civil Lines, Ramdaspeth, Laxmi Nagar, Bajaj Nagar, Wardha Road, Manish Nagar and nearby areas.

Contact Kumar Sir for one-to-one Physics classes.

Phone / WhatsApp: +91-9958461445
Website: kumarphysicsclasses.com
Email: kumarsirphysics@gmail.com