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- 1. a. Show that the potential energy is U = ? p ? ? E ? , up to a constant. b. Compute the "force" associated with this energy. That is, define the angle ?? between the field and the dipole moment, and compute -dU/d ??. Show that this is actually the torque on the dipole. Solution Since dipole moment P=qd. Potential energy is defined as the work done i bringing the charge from infinity to the given position. Hence, potential energy of dipole moment is pEcosÂ© where ?? is dipole moment, ? is uniform electric field and Â© is angle between dipole moment and electric field. Work done in rotating a dipole mtoment in electric field is also termed as energy of the dipole. Thus, dU = pXEdÂ© = p*E*sinÂ©*dÂ© Hence, U= integration of dU within proper limit Thus, we get, U=p*E(cosÂ©Â¹ - cosÂ©Â²)