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?

Explanation

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
`V=kQ/r`
`=(8.99xx10^9 N⋅m^2/C^2)((−3.00xx10^(−9) C)/(5.00xx10^(−2) m)`
` =−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.