The big idea: Pull a jumper off over your head in the dark and you hear it crackle — you've rubbed electric charge from one surface onto another.
Charge in three facts
- Charge comes in two kinds: positive and negative (unit: the coulomb, C).
- Like charges repel (push apart); unlike charges attract (pull together).
- Objects charge up when electrons (tiny negative particles) move from one object to another.
The electric field around a positive charge points outward — it pushes another positive charge away. (For a negative charge the arrows point inward, towards it.) The lines spread out, so the force gets weaker further away.
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Three ways to charge something: Friction — rub two materials so electrons rub off one onto the other.
Contact — touch a charged object so charge flows across.
Induction — bring a charge near (no touching) and ground the object; it keeps the opposite charge.
| Method | What you do | What happens |
|---|---|---|
| Friction (rubbing) | Rub two different materials together (e.g. a cloth on a rod). | Electrons are transferred from one to the other — one ends up negative, the other positive. |
| Contact | Touch a charged object onto a neutral one. | Some charge flows across until they share it — both end up with the same sign of charge. |
| Induction | Bring a charge near (not touching), then ground the far side and remove the ground. | The object keeps an opposite charge to the one brought near — without ever touching it. |
Charging by induction, step by step
Conservation of charge: Charge is never created or destroyed — it only moves.
If one object gains a charge of −q, the object it took electrons from is left with +q. The total stays the same.
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Coulomb's law gives the force between two point charges. The force grows with the charges and shrinks with the square of the distance between them:
- electric force between the charges (N)
- Coulomb constant, 8.99 × 10⁹ N m² C⁻²
- the two point charges (C, coulombs)
- distance between the charges (m)
Where k comes from: k = 1/(4πε₀), where ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻² is the permittivity of free space (both in the data booklet).
In a material the charges sit in, use its permittivity ε instead of ε₀: a larger permittivity gives a smaller force.
Which way does the force point?: The size comes from the formula; the direction comes from the signs.
Same signs (+ and +, or − and −) → the charges repel (push apart).
Opposite signs (+ and −) → the charges attract (pull together).
Two point charges, q1 = 2.0 × 10⁻⁶ C and q2 = 3.0 × 10⁻⁶ C, sit 0.20 m apart. Find the force between them. (k = 8.99 × 10⁹ N m² C⁻².)
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Touching identical spheres
Contact shares charge equally: When two identical conducting spheres touch, the total charge is shared equally between them (charge is conserved).
So +Q and −2Q become −Q/2 each. Then use Coulomb's law again with the new charges.
Two identical small conducting spheres carry +6.0 nC and −2.0 nC and attract each other with a force F. They are touched together and returned to the same separation. Find the new force in terms of F, and state whether it attracts or repels.
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How this is tested — Coulomb's law and charging open the Fields theme:
Paper 1A
- Quick inverse-square reasoning — how the force changes when a charge is halved/doubled or the separation changes.
- Or the sign of an induced charge after grounding.
Paper 2
- Calculate the force F = k q1q2/r² between point charges.
The classic trap: Forgetting the square — halving the separation multiplies the force by 2² = 4, not by 2.
The scaling shortcut: Because F is proportional to q1q2 and to 1/r², you don't always need k.
Halve one charge → F is halved. Double the separation → F is divided by 2² = 4. Combine the effects step by step.
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Two point charges a fixed distance apart exert a force of 8.0 N on each other. (a) One charge is replaced by another of half its size, separation unchanged — find the new force. (b) Instead, starting again from 8.0 N with both charges unchanged, the charges are moved to twice their original separation — find the new force.
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