A small, isolated, uncharged conducting ball bearing of radius sits inside an…
PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Conductors, capacitance and boundary-value electrostatics · Conductors, capacitance and boundary-value electrostatics
The Boundary-Value Problem, Ch Separation of variables in spherical geometry
Problem
A small, isolated, uncharged conducting ball bearing of radius a=3.0×10−3m sits inside an electrostatic precipitator, in a region where the field would be uniform, E0=8.0×105V m−1, if the ball were not there. The ball is far from the precipitator's walls, so the field it distorts is otherwise uniform. For a ball bearing of this radius, sharp local corona discharge is found to begin once the surface field reaches Eonset=6.0×106V m−1.
((a)) Find the electric field at the poles of the ball (the points closest to and farthest along the applied field direction), and state whether corona discharge occurs there.
((b)) Find the induced dipole moment of the ball.
((c)) The permanent dipole moment of an ammonia molecule is 1.5×10−30C m. Express the ball's induced dipole moment as a multiple of this, to two significant figures.