Physics / Unit 9: Electricity and Circuits
9.2 Coulomb's Law
Notes
Coulomb's law gives the electric force between two point charges: $\displaystyle F = \frac{k q_1 q_2}{r^2}$.
- $k = 9.0 \times 10^9 \text{ N·m}^2/\text{C}^2$.
- Like gravity, it is an inverse-square law: double the distance and the force becomes one fourth.
- Unlike gravity, it can attract or repel, and it is far stronger.
- Example: two $2.0 \times 10^{-6} \text{ C}$ charges 0.30 m apart: $\displaystyle F = \frac{(9.0 \times 10^9)(2.0 \times 10^{-6})^2}{0.30^2} = \frac{0.036}{0.09} = 0.40 \text{ N}$.
Practice
Two charges are moved so the distance between them is cut in half. The electric force becomes:
$\displaystyle F \propto \frac{1}{r^2}$, and $\displaystyle \frac{1}{(1/2)^2} = 4$.
A $+3 \times 10^{-6} \text{ C}$ charge and a $-3 \times 10^{-6} \text{ C}$ charge are 0.3 m apart. What is the force between them?
$\displaystyle F = \frac{(9.0 \times 10^9)(3 \times 10^{-6})^2}{0.09} = \frac{0.081}{0.09} = 0.9 \text{ N}$; opposite charges attract.
One charge is doubled and the other is tripled, with the same distance. The force becomes:
$F \propto q_1q_2$, so $2 \times 3 = 6$.
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