V P = k ∑ 1 N q i r i = ( 9.0 × 10 9 N.You can easily show this by calculating the potential energy of a test charge when you bring the test charge from the reference point at infinity to point P:įigure 7.20 A general diagram of an electric dipole, and the notation for the distances from the individual charges to a point P in space.Īpply V P = k ∑ 1 N q i r i V P = k ∑ 1 N q i r i to each of these three points. Then, the net electric potential V P V P at that point is equal to the sum of these individual electric potentials. Let V 1, V 2, …, V N V 1, V 2, …, V N be the electric potentials at P produced by the charges q 1, q 2, …, q N, q 1, q 2, …, q N, respectively.
What is the net electric potential V at a space point P from these charges? Each of these charges is a source charge that produces its own electric potential at point P, independent of whatever other changes may be doing. Consider a system consisting of N charges q 1, q 2, …, q N. Just as the electric field obeys a superposition principle, so does the electric potential. As noted earlier, this is analogous to taking sea level as h = 0 h = 0 when considering gravitational potential energy U g = m g h U g = m g h. It is the potential difference between two points that is of importance, and very often there is a tacit assumption that some reference point, such as Earth or a very distant point, is at zero potential. Ground potential is often taken to be zero (instead of taking the potential at infinity to be zero). The voltages in both of these examples could be measured with a meter that compares the measured potential with ground potential. Check Your Understanding What is the potential inside the metal sphere in Example 7.10?
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