Example 19.6 from College Physics, 19.3 Electrical Potential Due to a Point Charge

What Voltage Is Produced by a Small Charge on a Metal Sphere?

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?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

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 $V = kQ / r$ .
Solution

Entering known values into the expression for the potential of a point charge, we obtain

$\begin{array}{l} V & = & k \frac{Q}{r} \\ = & (8.99 \times 10^{9} N \cdot m^{2} / C^{2}) (\frac{–3.00 \times 10^{–9} C}{5.00 \times 10^{–2} m}) \\ = & –539 V. \end{array}$
19.40
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.

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Solution

Discussion

Strategy

Solution

Discussion