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 pEcos© where ?? is dipole moment, ? is uniform electric field and © 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 = pXEd© = p*E*sin©*d© Hence, U= integration of dU within proper limit Thus, we get, U=p*E(cos©¹ - cos©²) .

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 pEcos© where
?? is dipole moment, ? is uniform electric field and © 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 = pXEd© = p*E*sin©*d©
Hence, U= integration of dU within proper limit
Thus, we get, U=p*E(cos©¹ - cos©²)