Question

Two different conducting objects, initially separated, are connected by a conducting wire. When the wire is removed, can you conclude that the two objects: (a) carry the same net charge; (b) are at the same potential; (c) have the same charge and the same potential; or (d) have neither the same charge nor potential? Explain.

Answer 1

The two objects after (b) are at the same potential

Explanation:

When the two conducting objects are connected together, charge will be transferred from one object ot another until the two objects reach the same potential.

In fact, if there is still some residual potential difference between the two objects, there would still be a net electric field pushing the charges from one object to the other. Therefore, equilibrium is reached only when the net electric field between the two objects becomes zero, and this occurs only when the potential difference is zero, so when the two objects are at the same potential.

At the equilibrium, however, the charge on the two objects can be different. In fact, the capacity of an object is given by

$C=\frac{Q}{V}$

where Q is the charge stored by an object and V is its potential. It can be re-arranged as

$Q=CV$

The two objects are at same potential, V, however their  capacity C can be different since the two objects are not identical: therefore, their stored charge can be different.

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