Successfully reported this slideshow.

# a- Show that the potential energy is U - - p - - E - - up to a constan.docx

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.
Hence, U= integration of dU within proper limit
.

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.
Hence, U= integration of dU within proper limit
.