Electrostatic charge and law of conservation of energy
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Dec26-09, 08:55 PM
You do a certain amount of work to charge up plate A. This is an easy exercise of bringing each charge in from infinity to its designated position, one charge at a time. But this is in the absence of our grounded plate B. Since B is in the picture here, you are doing more work, because when you bring in your charge from infinity to A, you also have to repel a charge from B to the ground. Remember, plate B was originally neutral, as you bring in an electron from infinity to A, you must also move an electron from A to ground in response to your induction.
EDIT: It would probably be enlightening to work it out on paper for the first charge. Essentially, you will be bringing in a charge to plate A and inducing a growing "dipole moment" in B as you move an electron away in response and leave behind a positive charge. This seems conceptually similar to the polarization of a dielectric. In a dielectric, an applied field induces dipole moments in the dielectric. These dipole moments store energy and the equivalent energy stored is taken out of the net electric field by the opposing field induced by the dipole moment.
Assume A was made to gain charge when B was not around...after it did gain the desired charge, B was put in the picture. It was bought close unearthed, then at a certain distance, B was earthed.