MODULE 06 · E1 / UNIT 1 · ELECTROSTATICS
Electric Charge and Coulomb’s Law
Like charges repel, unlike charges attract, and the force falls off with the square of the distance.
POINT CHARGES ON A PLANE · DRAG OR USE THE ARROW KEYS
Learning objective
Conditions · locked for this activity
The plane
ReadyPoint charges at rest on a 1.0 m × 0.6 m plane, in vacuum. Each arrow is the electric force on the charge it starts from. F₁₂ means the force on q₁ due to q₂. Arrow lengths are proportional to force (scale bar, top right); press Rescale arrows after big changes.
Force graph
LIVEThe curve is F = k|q₁q₂|/r² for q₁ and q₂. The dot is the present distance; the hollow dot is the previous one.
| Charge | |F| (N) | Fx | Fy |
|---|
Key ideas
ALGEBRA| Charge is quantized | q = n e, e = 1.602 × 10⁻¹⁹ C | |
|---|---|---|
| Coulomb’s law | F = k |q₁q₂| / r² | |
| Coulomb constant | k = 8.988 × 10⁹ N·m²/C² | |
| Superposition | Fnet = F₁₂ + F₁₃ + … (vectors) |
Like charges repel and unlike charges attract. The forces between two charges are a Newton’s third law pair: equal in size and opposite in direction, even when one charge is much bigger. With several charges, add the pair forces as vectors, component by component.
Show the calculus
Turn on for Coulomb’s law in vector form and the force from a charged rod, found by integrating over the charge.
F₁₂ = k q₁q₂ (r₁ − r₂) / |r₁ − r₂|³
| r₁ − r₂ | |
|---|---|
| F₁₂ (vector) |
A uniformly charged rod
F = ∫₀ᴸ k λ q dx / (L + d − x)² = k Q q / [d (d + L)]
| Exact integral | |
|---|---|
| Sum of n point-charge slices | |
| All of Q at the centre, kQq/(d + L/2)² |
The point charge is q = +2 μC. Increase n and the sum approaches the integral. Increase d far beyond L and the rod acts like a point charge at its centre. Close to the rod, the near end dominates and the point-charge estimate is too small.
Charging: friction, contact and induction
ELECTROSCOPEEach + or − symbol stands for a very large number of elementary charges (about 10⁹ e). Only electrons move; the positive charges stay fixed in the atoms. The total never changes: charging moves charge, it does not create it.
Results
Reflect on the evidence
Instructor-authored model answer
SI units, k = 8.988 × 10⁹ N·m²/C². Charges are points held at rest; forces are computed exactly from Coulomb’s law and added as vectors. Charges cannot be placed closer than 4 cm.