The Force of Static Electricity
Formulated by French physicist Charles-Augustin de Coulomb in 1785, Coulomb's Law is the fundamental equation that describes the electrostatic force between two electrically charged particles.
It states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. This means if you move two charged particles twice as far apart, the force between them drops to a mere one-quarter of its original strength.
The Inverse-Square Nature of the Universe
Coulomb's Law is mathematically almost identical to Newton's Law of Universal Gravitation. Both are "inverse-square" laws. However, there is one massive difference: gravity only ever attracts, but the electrostatic force can attract or repel.
Like charges (two protons, or two electrons) violently repel each other. Opposite charges (a proton and an electron) violently attract each other. Furthermore, the electrostatic force is unimaginably stronger than gravity—roughly $10^{36}$ times stronger!
Everyday Electrostatics
- Static Cling: When you rub a balloon on your hair, you are physically scraping negatively charged electrons off your hair and onto the rubber. Your hair (now net positive) and the balloon (net negative) fiercely attract each other via Coulomb's force, causing your hair to stand on end.
- Chemistry: The entire field of chemistry is effectively just applied Coulomb's law. Chemical bonds are formed entirely by the electrostatic attraction between the positively charged nucleus of one atom and the negatively charged electrons of another.
- Laser Printers: A laser creates a perfectly patterned static electric charge on a rotating drum. Negatively charged toner powder is pulled by Coulomb's force exclusively onto those positively charged spots, perfectly transferring the image onto the paper.
The Formula
Example Calculation
You have two small metal spheres. Sphere A has a positive charge of $+2 \times 10^{-6} , \text{C}$ ($2 , \mu\text{C}$). Sphere B has a negative charge of $-5 \times 10^{-6} , \text{C}$ ($-5 , \mu\text{C}$). They are separated by $0.1 , \text{meters}$ ($10 , \text{cm}$). Coulomb's constant ($k$) is roughly $8.99 \times 10^9$.
- Multiply Charges ($|q_1 \cdot q_2|$): $| (2 \times 10^{-6}) \cdot (-5 \times 10^{-6}) | = 10 \times 10^{-12}$.
- Multiply by Constant ($k$): $(8.99 \times 10^9) \cdot (10 \times 10^{-12}) = 0.0899$.
- Divide by Distance Squared ($r^2$): $0.0899 / (0.1)^2 = 0.0899 / 0.01 = 8.99 , \text{Newtons}$.
The two spheres attract each other with a force of exactly $8.99 , \text{Newtons}$ (roughly the weight of a 2-pound weight). Because one is positive and one is negative, the force pulls them together.