A dipole refers to a pair of equal and opposite charges (+q and -q) separated by a small distance (2a). The dipole is characterised by a quantity called the electric dipole moment (p). It is a vector quantity defined as:
p = q × 2a
The direction of dipole moment is from negative charge to positive charge.
Dipole in a Uniform External Electric Field
When a electric dipole is placed in uniform electric field, its two charges experience equal and opposite forces, which cancel each other and hence net force on electric dipole in uniform electric field is zero.
Torque on the Dipole
No Net Force on the Dipole
Force on the Dipole
In a uniform field, the electric field E is the same at both ends of the dipole. Since one end has a charge +q and the other has –q, the electric field exerts a force on each charge.
The positive charge experiences a force F = qE in the direction of the field.
The negative charge experiences a force F = –qE in the opposite direction.
These two forces are equal in magnitude but opposite in direction and act along parallel lines.
As a result, the net force on the dipole is zero. That means the dipole does not move linearly in the field it stays in place or may rotate.
Torque on the Dipole
Although the net force is zero, the forces do not cancel out completely because they act at different points (they are not collinear). This creates a turning effect, known as torque.
The torque (τ) tries to rotate the dipole to align with the direction of the electric field.
Mathematically, torque is given by:
τ = p × E
Or in scalar form:
τ = pE sin θ
Where:
τ is the torque,
p is the magnitude of the dipole moment,
E is the strength of the electric field,
θ is the angle between the dipole moment and the electric field.
So, the torque is maximum when the dipole is perpendicular to the field (θ = 90°) and zero when the dipole is aligned or anti-aligned with the field (θ = 0° or 180°).
Potential Energy of a Dipole in an Electric Field
A dipole in an electric field also has potential energy (U), depending on its orientation.
U = −p ⋅E = −pE cos θ
The potential energy is minimum (most stable) when the dipole is aligned with the field (θ = 0°).
It is maximum (least stable) when the dipole is opposite to the field (θ = 180°).
Real-Life Similarity
Imagine a compass needle (which is also a dipole, but magnetic) in Earth’s magnetic field. The needle rotates until it points in the direction of the magnetic field. Similarly, an electric dipole rotates in an electric field to align with it.
Key Points
A dipole in a uniform electric field experiences no net force, but experiences a torque that tends to align it with the field.
The torque depends on the dipole moment, field strength, and the angle between them.
The potential energy of the dipole is lowest when aligned with the field and highest when opposite to it.
This concept is critical in understanding of molecular behaviour in fields, electrical instrumentation, and more.
An electric dipole consists of two equal and opposite charges (+q and –q) separated by a small fixed distance (2a). It is characterized by a vector quantity called the electric dipole moment (p = q × 2a), directed from the negative to the positive charge.
When a dipole is placed in a uniform electric field:
It experiences no net force, because the forces on +q and –q cancel out.
It experiences a torque, which tends to align the dipole with the electric field direction.
The electric field exerts equal and opposite forces on the two charges of the dipole. Since the field is uniform (same magnitude and direction everywhere), the net force cancels out, resulting in zero linear motion of the dipole.
The torque τ acting on a dipole in a uniform electric field is given by:
τ = p × E
In magnitude:
τ = pE sin θ
Where θ is the angle between the dipole moment vector and the electric field.
Maximum torque occurs when the dipole is perpendicular to the field (θ = 90°).
Zero torque occurs when the dipole is either parallel or anti-parallel to the field (θ = 0° or 180°).
The potential energy U of a dipole in an electric field is given by:
U = −p ⋅ E = −pE cos θ
It is:
Minimum (most stable) when θ = 0° (aligned with field),
Maximum (least stable) when θ = 180° (opposite to field).