Electric Dipole in Electric Fields – Key Vocabulary

Vocabulary flashcards summarising essential terms and formulas related to electric dipoles in uniform and non-uniform electric fields, equilibrium positions, potential energy, small oscillations, and interactions.

Electric Dipole

A system of two equal and opposite charges (+q and –q) separated by a small fixed distance.

Dipole Moment (P)

Vector quantity defined as q d (charge × separation), directed from the negative to the positive charge.

Uniform Electric Field

An electric field that has the same magnitude and direction at every point in the region.

Torque on an Electric Dipole

τ = P × E; its magnitude is τ = P E sin θ, where θ is the angle between P and E.

Couple (Dipole in Field)

Two equal and opposite forces acting on the charges, producing a pure torque with no net translational force.

Net Force in Uniform Field

For a pure dipole, Fnet = 0 and the centre of mass has zero translational acceleration (acm = 0).

Equilibrium Orientation

Orientations where τ = 0, i.e., θ = 0° (parallel) or θ = 180° (antiparallel) with the electric field.

Stable Equilibrium

θ = 0°; a small angular displacement produces a restoring torque back toward equilibrium.

Unstable Equilibrium

θ = 180°; a small angular displacement increases the departure from equilibrium.

Potential Energy of a Dipole

U = –P · E cos θ = –P E cos θ, the energy associated with the dipole’s orientation in a uniform field.

Minimum Potential Energy

U_min = –P E at θ = 0°, corresponding to stable equilibrium.

Maximum Potential Energy

U_max = +P E at θ = 180°, corresponding to unstable equilibrium.

Small Angular Oscillations

For small θ, the dipole executes simple harmonic motion with equation I α = –P E θ.

Angular Frequency (ω)

ω = √(P E / I) for small oscillations of a free dipole about the stable position.

Time Period (Free Dipole)

T = 2π √(I / P E) when the dipole oscillates about its centre of mass.

Time Period (Hinged Dipole)

T = 2π √(I_pivot / P E) when the dipole is pivoted at one end.

Work Done by External Agent

Wext (slow rotation) = Ufinal – Uinitial = –P E (cos θf – cos θ_i).

Maximum Angular Speed

Obtained from energy conservation: ½ I ωmax² = Uinitial – U_final.

Dipole in Non-Uniform Field

Experiences a net force F = (P · ∇)E; direction depends on the gradient of E.

Force Along x-Axis

If P is along x and E varies with x, F = P (dE/dx).

Force Between Two Collinear Dipoles

Magnitude F = 2 k P₁ P₂ / r⁴ (attraction or repulsion depends on relative orientations).

Electric Dipole

A system of two equal and opposite charges (+q and –q) separated by a small fixed distance.

Dipole Moment (P)

Vector quantity defined as q d (charge × separation), directed from the negative to the positive charge.

Uniform Electric Field

An electric field that has the same magnitude and direction at every point in the region.

Torque on an Electric Dipole

τ = P × E; its magnitude is τ = P E sin θ, where θ is the angle between P and E.

Couple (Dipole in Field)

Two equal and opposite forces acting on the charges, producing a pure torque with no net translational force.

Net Force in Uniform Field

For a pure dipole, Fnet = 0 and the centre of mass has zero translational acceleration (acm = 0).

Equilibrium Orientation

Orientations where τ = 0, i.e., θ = 0° (parallel) or θ = 180° (antiparallel) with the electric field.

Stable Equilibrium

θ = 0°; a small angular displacement produces a restoring torque back toward equilibrium.

Unstable Equilibrium

θ = 180°; a small angular displacement increases the departure from equilibrium.

Potential Energy of a Dipole

U = –P · E cos θ = –P E cos θ, the energy associated with the dipole’s orientation in a uniform field.

Minimum Potential Energy

U_min = –P E at θ = 0°, corresponding to stable equilibrium.

Maximum Potential Energy

U_max = +P E at θ = 180°, corresponding to unstable equilibrium.

Small Angular Oscillations

For small θ, the dipole executes simple harmonic motion with equation I α = –P E θ.

Angular Frequency (ω)

ω = √(P E / I) for small oscillations of a free dipole about the stable position.

Time Period (Free Dipole)

T = 2π √(I / P E) when the dipole oscillates about its centre of mass.

Time Period (Hinged Dipole)

T = 2π √(I_pivot / P E) when the dipole is pivoted at one end.

Work Done by External Agent

Wext (slow rotation) = Ufinal – Uinitial = –P E (cos θf – cos θ_i).

Maximum Angular Speed

Obtained from energy conservation: ½ I ωmax² = Uinitial – U_final.

Dipole in Non-Uniform Field

Experiences a net force F = (P · ∇)E; direction depends on the gradient of E.

Force Along x-Axis

If P is along x and E varies with x, F = P (dE/dx).

Force Between Two Collinear Dipoles

Magnitude F = 2 k P₁ P₂ / r⁴ (attraction or repulsion depends on relative orientations).