Charges in static electricity are typically in the nanocoulomb (nC) to microcoulomb (μC) range. What is the voltage 5.00 cm away from the center of a 1-cm diameter metal sphere that has a −3.00 nC static charge?
Strategy
As we have discussed in Electric Charge and Electric Field, charge on a metal sphere spreads out uniformly and produces a field like that of a point charge located at its center. Thus we can find the voltage using the equation V = kQ / r .
Entering known values into the expression for the potential of a point charge, we obtain
V=k \frac{Q}{r} (19.40)
=\left(8.99 \times 10^{9} N \cdot m ^{2} / C ^{2}\right)\left(\frac{-3.00 \times 10^{-9} C }{5.00 \times 10^{-2} m }\right)= –539 V.
Discussion
The negative value for voltage means a positive charge would be attracted from a larger distance, since the potential is lower (more negative) than at larger distances. Conversely, a negative charge would be repelled, as expected.