In a uniform electric field , a perfectly conducting particle having radius has a dipole moment…
In a uniform electric field 
, a perfectly conducting particle having radius 
has a dipole moment 
Provided that is short compared to distances over which the field varies, this gives a good approximation to 
, even where the field is not uniform. Such a particle is shown at the location 
in Fig. P11.8.1, where it is subject to the field produced by a periodic potential 
cos(
) imposed in the plane 
(a) Show that the potential imposed in the region 
is 
cos() exp (
). (b) Show that, provided that the particle has no net charge, the force on the particle is
Fig. P11.8.1
