Answer to Question #200958 in Field Theory for Mallory

Question

A metallic table tennis ball of mass 0.127 g has a charge of 7.3E-6 C.  What potential difference is required to hold the table tennis ball in suspension across a large parallel plate apparatus with plate separation of 20.0 cm.

Answer 1

In order to hold the table tennis ball in suspension across a large parallel plate apparatus the force of gravity acting on the ball must be balanced by the electric force:

$$F_e=F_g,$$ $$qE=mg,$$ $$\dfrac{q\Delta V}{d}=mg,$$ $$\Delta V=\dfrac{mgd}{q},$$ $$\Delta V=\dfrac{1.27\cdot10^{-4}\ kg\cdot9.8\ \dfrac{m}{s^2}\cdot0.2\ m}{7.3\cdot10^{-6}\ C}=34\ V.$$