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CISCEISC (Science) ISC Class 12
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Syllabus

Motion of an Electric Dipole in a Uniform Electric Field

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Estimated time: 8 minutes
CISCE: Class 12

Introduction

An electric dipole consists of two equal and opposite point charges (+q and −q) separated by a small distance (2a). When placed in an external electric field, its behavior differs sharply depending on whether the field is uniform or non-uniform.

CISCE: Class 12

Key Terms

Term Definition
Electric Dipole Moment (p) Product of magnitude of charge (q) and separation (2a): p = q × 2a, directed from −q to +q.
Uniform Electric Field A field with the same magnitude and direction at every point in space.
Torque (τ) Turning effect of a force; here it rotates the dipole to align \[\vec p\]​ with \[\vec E\].
Restoring Couple The torque that tends to restore/align the dipole along the field direction.
Dipole Potential Energy (U) Energy possessed by the dipole due to its orientation in the field.
CISCE: Class 12

Force on a Dipole in a Uniform Field

  • Force on +q: F1 = qE (along \[\vec E\])
  • Force on −q: F2 = qE (opposite to \[\vec E\])

Since both forces are equal in magnitude and opposite in direction:

Fnet = qE − qE = 0

Net force on a dipole in a uniform field is always zero — hence no translational motion occurs.

CISCE: Class 12

Torque on the Dipole

Although net force is zero, the two forces act at different points, forming a couple, which produces torque:

τ = pE sin ⁡θ

In vector form:

\[\vec τ\] = \[\vec p\] × \[\vec E\]

Where θ is the angle between \[\vec p\]​ and \[\vec E\].

Special Cases Table

 
Angle (θ) Torque Value Physical Meaning
0° τ = 0 \[\vec p\]​ parallel to \[\vec E\] — stable equilibrium
90° τ = pE (maximum) Dipole experiences maximum turning effect
180° τ = 0 \[\vec p\]​ antiparallel to \[\vec E\] — unstable equilibrium
CISCE: Class 12

Potential Energy of a Dipole

Work done to rotate the dipole from θ' to θ against the restoring torque gives potential energy:

U = −pE cos⁡ θ

Key Values

Orientation (θ) Potential Energy (U) Stability
0° U = −pE (minimum) Stable equilibrium
90° U = 0 Neutral point
180° U = +pE (maximum) Unstable equilibrium

Minimum PE = most stable orientation. Maximum PE = least stable orientation.

CISCE: Class 12

Uniform vs Non-Uniform Field — Comparison Table

Feature Uniform Field Non-Uniform Field
Net Force Zero Non-zero
Net Torque Non-zero (unless θ = 0°/180°) Present
Motion Type Rotational only Rotational and translational
Example Field between parallel plates Field near a point charge
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