Physics · Electrostatic Potential And Capacitance · NEET
The minus sign in U = -pE cosθ just tells you the direction of the energy compared to the θ = 90° reference. When the dipole is aligned with the field (θ = 0), cosθ = 1, so U = -pE, a negative (minimum) value. Nature always pushes systems toward lowest energy, so the dipole is 'happy' and stable when aligned — that is why U is most negative there. It is not saying energy is 'missing'; it means work was released as the dipole turned into the field.
θ is the angle between the dipole moment vector p (which points from the -q charge to the +q charge) and the external field E. It is NOT the angle with any wall or plate. Always draw the p arrow first, then measure how far it is tilted from E. θ = 0 means p points along E; θ = 180° means p points opposite to E.
By convention we bring the dipole in from the θ = 90° (perpendicular) position because there the field does no net work while rotating the dipole into place (torque is balanced in a symmetric way). Putting U = 0 at 90° makes the formula clean: U = -pE cosθ, which gives -pE at 0° and +pE at 180°. This is the NCERT-chosen reference, so use it for NEET.
Torque τ = pE sinθ is the turning effect that tries to rotate the dipole; it is largest at θ = 90° and zero at 0° and 180°. Potential energy U = -pE cosθ is the stored energy; it is lowest at 0° and highest at 180°. Torque is a vector (a cause of rotation); U is a scalar (a stored amount). Both come from the same p and E but answer different questions.
Use ΔU = U(θ₂) - U(θ₁) = -pE(cosθ₂ - cosθ₁) = pE(cosθ₁ - cosθ₂). This ΔU equals the work you must do to rotate it (against the field). Example: from θ₁ = 0° to θ₂ = 60°, ΔU = pE(cos0° - cos60°) = pE(1 - 0.5) = 0.5 pE.
An electric dipole with dipole moment 5 × 10⁻⁶ C·m is aligned with the direction of a uniform electric field of magnitude 4 × 10⁵ N/C. The dipole is then rotated through an angle of 60° with respect to the electric field. The change in the potential energy of the dipole is:
A dipole is placed in an electric field (as shown in the figure). In which direction will it move?
Try the real previous-year questions from this chapter — each with the answer and a full solution.
U = -pE cosθ, or in vector form U = -p·E, where p is the dipole moment, E is the field, and θ is the angle between them. It gives -pE at θ = 0° and +pE at θ = 180°.
At θ = 0°, when the dipole is aligned with the field. Then cosθ = 1 and U = -pE, the minimum (most negative) value. This is the stable equilibrium position.
Zero. At θ = 90°, cos90° = 0, so U = -pE(0) = 0. This perpendicular position is the chosen reference from which PE is measured.
θ = 0° (aligned with E) is stable — lowest energy, torque restores it if disturbed. θ = 180° (anti-parallel to E) is unstable — highest energy, any small push turns it away.
No. In a uniform field the two charges feel equal and opposite forces, so net force is zero — only a torque acts. A net force appears only in a non-uniform field, which is why PE changes and the dipole drifts toward stronger field.
Strictly, U = -pE cosθ is derived for a uniform field. In a non-uniform field the field varies over the dipole, so a net force also appears, but for NEET the principle 'the dipole moves to lower U = -p·E' still guides the answer.
