Coulomb's law
Push and pull across empty space
- Two charges push or pull each other without ever touching.
- Coulomb's law gives the exact size of that force.
- It looks remarkably like Newton's law of gravity.
Coulomb's law
- $F = \dfrac{Q_1 Q_2}{4\pi\varepsilon_0 r^{2}}$, along the line joining the charges.
- Like charges repel; opposite charges attract. ($\varepsilon_0 = 8.85 \times 10^{-12}\ \dfrac{\text{F}}{\text{m}}$.)
Practice
Coulomb's law gives the force between two point charges as:
Proportional to each charge, inversely proportional to the distance squared.
Practice
Two charges of the same sign repel each other.
Like charges repel; opposite charges attract — both along the line joining them.
An inverse-square law
- The force falls off as $\dfrac{1}{r^{2}}$.
- Treble the separation → the force drops to a ninth.
Practice
Two charges repel with $36\ \text{N}$ at separation $r$. What is the force at separation $3r$?
Inverse-square: $\dfrac{36}{3^{2}} = \dfrac{36}{9} = 4\ \text{N}$.
Practice
Coulomb's law is an ____-square law (the force is proportional to 1/r²).
Force $\propto \dfrac{1}{r^{2}}$ — the same distance dependence as gravity.
Spheres and conductors
- Outside, a charged sphere acts like a point charge at its centre.
- Inside a hollow charged conductor, the field is zero.
Practice
Select all the true statements.
Like charges repel (not attract). The other three are all correct.
You've got it
Key idea
- Coulomb: $F = \dfrac{Q_1 Q_2}{4\pi\varepsilon_0 r^{2}}$ — like repel, opposite attract
- it is inverse-square (like gravity, but it can repel)
- a charged sphere acts as a point charge outside; field is zero inside a hollow conductor