Spring 2010 Solutions - FSU Physics Department

Problem 8A parallel plate capacitor with capacitance C is charged to a potential difference V and is thendisconnected from the charging source. The capacitor has an area A and a plate separationz. Neglect fringe effects at the edges of the plates.(a) What is the force acting on the upper capacitor plate as a function of plateseparation z?(b) Assume now that a glass plate of the same area A completely fills the spacebetween the plates. The glass has a dielectric constant κ. How much work isrequired to pull the glass plate out of the capacitor?SOLUTION:A parallel plate capacitor with capacitance C is charged to a potential difference V and isthen disconnected from the charging source. The capacitor has an area A and a plateseparation z.(a) What is the force acting on the upper capacitor plate as a function of plateseparation z?When the capacitor is disconnected from the charging source, thecharge on the capacitor plates stays constant. The force o thecapacitor plate can be written asdWF =−|dzQ = const.Where W is the stored energy in the capacitor. W is given byW21 Q=2 CThe capacitance C may be writtenCA= ε0zwhich can be substituted in to give2 21 Q 1 Q zW = =2 C 2 ε AInserting this into the force equation:02 2dW d ⎛1Q z ⎞ QF =− =− ⎜ ⎟= −dz dz ⎝2 ε0A ⎠ 2ε0A