Physics · Electrostatic Potential And Capacitance · NEET
Yes. In a uniform field the electric force does no net work in moving the dipole, only rotation matters. The external work you do to rotate the dipole slowly equals the change in its potential energy: W = U2 - U1 = pE(cos theta1 - cos theta2). This is because U = -pE cos theta, so W = (-pE cos theta2) - (-pE cos theta1) = pE(cos theta1 - cos theta2).
The dipole has the LOWEST energy when it is aligned with the field (theta = 0), because that is the stable position. Setting U minimum at theta = 0 forces the minus sign: at theta = 0, U = -pE (lowest); at theta = 180, U = +pE (highest, unstable). The minus sign encodes that aligning with the field releases energy.
Use W = pE(cos theta1 - cos theta2) = pE(cos0 - cos90) = pE(1 - 0) = pE. So it takes exactly pE joules of work to turn a dipole from fully aligned to perpendicular. This is a very common NEET plug-in.
W = pE(cos0 - cos180) = pE(1 - (-1)) = 2pE. Flipping a dipole completely against the field takes 2pE - the maximum possible work, moving it from the most stable to the most unstable position.
When a dipole rotates FROM a large angle TOWARD alignment (theta decreasing toward 0), the field's torque does POSITIVE work and potential energy DECREASES. When you rotate it AWAY from alignment, you (external agent) do positive work and PE increases. Always track who is doing the work: field vs external agent have opposite signs.
An electric dipole with dipole moment 5 x 10^-6 C.m is aligned with the direction of a uniform electric field of magnitude 4 x 10^5 N/C. The dipole is then rotated through an angle of 60 degrees with respect to the electric field. The change in the potential energy of the dipole is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
W = pE(cos theta1 - cos theta2), where theta1 is the initial angle and theta2 is the final angle between the dipole moment and the field. This equals the change in potential energy U2 - U1.
U = -pE cos theta = -(p . E) as a dot product. It is minimum (-pE) when aligned (theta = 0) and maximum (+pE) when antiparallel (theta = 180 degrees).
In a uniform field the net force on a dipole is zero (equal and opposite forces on +q and -q), so no translational work is done. Work appears only when you change the orientation (rotate it).
W = pE(cos90 - cos180) = pE(0 - (-1)) = pE joules.
No. Torque tau = pE sin theta is the turning effect at a given angle. Work is the integral of torque over the rotation, which sums to W = pE(cos theta1 - cos theta2).
