Section 3.5: Point Charges
A point charge is a charge that is considered to be concentrated at a single point in space. All the concepts of Coulomb’s law, electric field, and electric potential are applied to point charges.
For a point charge \(Q\):
- Electric Force on a test charge \(q\): \[ F = k \frac{|Q q|}{r^2} \]
- Electric Field: \[ \vec{E} = k \frac{Q}{r^2} \hat{r} \]
- Electric Potential: \[ V = k \frac{Q}{r} \]
Point charges are idealizations; they allow simplified calculations in electrostatics.
Example: Force Between Two Point Charges
Two point charges, \(Q_1 = 4 \, \mu\text{C}\) and \(Q_2 = -2 \, \mu\text{C}\), are 0.3 m apart. Find the force on \(Q_1\) due to \(Q_2\).
\[
F = k \frac{|Q_1 Q_2|}{r^2} = \frac{(8.99\times10^9)(4\times10^{-6})(2\times10^{-6})}{0.3^2} \approx 0.7987\,\text{N}
\]
Direction: Attractive toward \(Q_2\) since charges are opposite.
Practice Problems
- Calculate the electric field at a point 0.5 m from a point charge +3 μC.
- Two point charges +5 μC and -3 μC are 0.4 m apart. Find the net force on each charge.
- Explain why a small test charge is used when measuring electric fields of point charges.
- Three point charges lie on a straight line. Determine the net electric force on the middle charge.
- A point charge +2 μC is placed at the center of a hollow spherical shell. What is the net force from the shell?