Imagine two point charges, each having magnitude Q. If they were brought together until they were touching, how would the equipotential lines change?

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Observe the animation above. Notice that as the two point charges approach each other, they look more and more like a single charge. Eventually the equipotential lines are indistinguishable from those made by a single point charge of magnitude 2Q.

The same is true when you observe two point charges from a sufficiently large distance. If your distance from the charges is significantly greater than their separation distance, you will not be able to tell them apart from a single point charge.


What use is this?

This can be a powerful and simple way to check any equations you derive. It illustrates an important observation: Any physical solution for a system of charges should approach the solution for a single charge as the point of observation becomes very far away from the source charges. This is true of both electric potential and the electric field.