Dipole in a Uniform External Field

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A dipole consists of two equal and opposite charges (+q and -q) separated by a small distance 2a. The dipole moment (p) is a vector quantity given by:
p  = q × 2a
The direction of the dipole moment is from the negative charge to the positive charge.
Dipole in a Uniform External Field-Positive charge
Positive charge

Dipole in a Uniform External Field

Now, imagine placing this dipole in a uniform external electric field (call it E). A uniform field means that the electric field strength is the same at every point in the region.

What Happens to the Dipole in the Field?

There are two main effects:
Force on the Dipole
Each charge experiences a force due to the electric field.
  • The positive charge (+q) experiences a force in the direction of the field:
F+ = qE  
  • The negative charge (-q) experiences a force in the opposite direction:
F− = −qE
Since both forces are equal in magnitude but opposite in direction, and they act at different points (separated by distance 2a), they cancel out translationally, i.e., there is no net force on the dipole. However, these two forces create a torque that tries to rotate the dipole.

Torque on the Dipole
This pair of forces forms what we call a couple. The torque (τ) caused by this couple tends to rotate the dipole so that it aligns with the electric field.

τ = p × E  
The magnitude of the torque is: τ = pE sin θ
Where:
  • p is the dipole moment,
  • E is the electric field strength,
  • θ is the angle between p and E.
So, if the dipole is not aligned with the field, it experiences a torque that tries to rotate it until it becomes aligned with the field (θ = 0°). At that point, the torque becomes zero, and the dipole reaches stable equilibrium.

Potential Energy of a Dipole in a Uniform Field

When you try to rotate the dipole away from the field direction, you are doing work against the torque. This work is stored as potential energy (U) in the dipole. The potential energy of a dipole in an electric field is given by:
U = −p ⋅ E = −pE cos θ
Some key points:
  • When θ = 0°, dipole is aligned with the field, and U is minimum (U = -pE) → most stable.
  • When θ = 180°, dipole is opposite to the field, and U is maximum (U = +pE) → least stable.
  • When θ = 90°, dipole is perpendicular to the field, and U = 0 → unstable equilibrium.

Real-Life Analogy

Suppose a dipole used as a bar magnet and the electric field as Earth’s magnetic field. When we hang the magnet to go, it rotates and aligns with the field. The same happens to a dipole in an electric field, it “wants” to align itself.

Summary

  • A dipole in a uniform electric field experiences no net force but experiences torque unless it is aligned.
  • The torque tries to rotate the dipole to align with the field direction.
  • The potential energy depends on the angle between the dipole moment and the field direction.
An electric dipole consists of two equal and opposite charges (+q and -q) separated by a small fixed distance. It is characterized by its dipole moment (p), which is a vector pointing from the negative to the positive charge.
 



The dipole experiences no net force but experiences a torque that tends to rotate it so that its dipole moment aligns with the direction of the electric field.
 


The torque (τ) is given by the vector product:
τ  = p × E  
Its magnitude is:
τ = pE sin θ
Where θ is the angle between the dipole moment p and the electric field E.
 
Because the forces on the two charges (+q and -q) are equal in magnitude and opposite in direction, they cancel each other out. Hence, the net translational force is zero, though a torque may exist.
 
The potential energy (U) of a dipole in an electric field is given by:
U = −p ⋅ E = −pE cos θ
It is minimum when the dipole is aligned with the field (θ = 0°) and maximum when anti-aligned (θ = 180°).



The dipole is in stable equilibrium when it is aligned with the electric field (θ = 0°), as the torque is zero and the potential energy is at a minimum.
 
The dipole moment vector (p) indicates the strength and direction of the dipole. Its direction is always from the negative charge to the positive charge and plays a key role in determining how the dipole interacts with external electric fields.

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