Static electricity
All matter has tiny charges: positive protons and negative electrons. Usually they balance, so the object is neutral. When two different materials are rubbed together, electrons move from one to the other. The one that gains electrons becomes negative; the one that loses them becomes positive. The charge stays on the object (it is static) because plastic and glass do not let it flow away.
Two rules: like charges repel, unlike charges attract. A charged rod also attracts a neutral piece of paper, because it pulls the opposite charge in the paper a little closer.
Coulomb's law gives the force between two small charges: F = k q₁ q₂ / r², with k = 9 × 10⁹ N m²/C². Double the distance and the force becomes four times smaller. Charge is measured in coulomb (C); one electron has charge 1.6 × 10⁻¹⁹ C.
Conductors (metals) let charge flow; insulators (plastic, glass, dry air) do not. Uses and dangers: photocopiers, paint sprays and dust filters use static charge; lightning is a huge discharge, and a lightning conductor on a tall building carries it safely to the ground.
Magnetism
A magnet attracts iron, nickel and cobalt. Its pull is strongest at the two ends, the poles: north (N) and south (S). Like poles repel, unlike poles attract. You can never get a single pole: cut a magnet in two and each piece has both poles.
The space around a magnet where its force is felt is the magnetic field. We draw it with field lines: they leave the north pole, go round, and enter the south pole. Lines close together mean a strong field. A compass is a tiny magnet that lines up with the field; it points north because the Earth itself is a big magnet.
Materials: magnetic (iron, steel, nickel, cobalt) are pulled; copper, wood, plastic are not. Soft iron becomes magnetic easily and loses it quickly (good for electromagnets); steel keeps it (good for permanent magnets).
Current and magnetism
In 1820 Hans Christian Ørsted saw a compass needle turn near a wire with current. So moving charge makes a magnetic field.
- Straight wire: the field is a set of circles around the wire. Direction by the right-hand grip rule: hold the wire with your right hand, thumb along the current; your fingers curl in the direction of the field. Bigger current or closer to the wire means a stronger field: B = μ₀ I / (2π r).
- Coil (solenoid): many turns make a field like a bar magnet. Put an iron core inside and you get an electromagnet, which you can switch on and off and make stronger with more turns or more current.
- Force on a wire in a field: if a wire with current is placed in a magnetic field it is pushed sideways with force F = B I L (when the wire is at right angles to the field). The direction is given by Fleming's left-hand rule. This push is what spins an electric motor.
Electromagnetic induction
In 1831 Michael Faraday found the reverse: a changing magnetic field makes a voltage. Move a magnet into a coil and a small voltage (emf) appears, so a current flows in a closed circuit. Hold the magnet still and nothing happens.
Faraday's law: induced emf = N × (change in magnetic flux ÷ time), or ε = N ΔΦ/Δt. To get a bigger emf: move the magnet faster, use a stronger magnet, or use more turns.
Lenz's law: the induced current flows in the direction that opposes the change that made it. (That is why it is harder to push a magnet into a closed coil: energy is being turned into electricity.)
Uses: a generator spins a coil in a field to make AC; a transformer uses a changing field in one coil to induce a voltage in another: Vs/Vp = Ns/Np; a dynamo lights a bicycle lamp; an induction cooker heats a pan by induced currents.
Try it: two small experiments
1. Static: rub a plastic pen on dry hair or wool for 20 seconds and bring it near tiny paper bits. Predict first: will a metal spoon do the same if you hold it in your hand? (It will not, because the charge flows away through you.)
2. Magnet and compass: bring a bar magnet near a compass. Turn the magnet around and watch the needle swing. Then wind a wire round a nail and connect it to a cell: can it pick up pins? Count how many more pins it picks up with twice as many turns.
Key formulas and definitions
- Coulomb's law: F = k q₁ q₂ / r², k = 9 × 10⁹ N m²/C²
- Charge of one electron: e = 1.6 × 10⁻¹⁹ C; Q = n × e
- Field round a long straight wire: B = μ₀ I / (2π r)
- Force on a wire in a field (at right angles): F = B I L
- Faraday's law: ε = N × ΔΦ / Δt
- Transformer: Vs / Vp = Ns / Np
Worked examples
1. Two small charges of 2 μC and 3 μC are 0.3 m apart in air. Find the force between them.
F = k q₁ q₂ / r² = 9 × 10⁹ × (2 × 10⁻⁶) × (3 × 10⁻⁶) ÷ (0.3)² = 9 × 10⁹ × 6 × 10⁻¹² ÷ 0.09 = 0.054 ÷ 0.09 = 0.6 N. If both are positive (or both negative) they repel.
2. A 0.3 m wire carries 4 A at right angles to a 0.5 T field. Find the force on it.
F = B I L = 0.5 × 4 × 0.3 = 0.6 N. Reverse the current and the force reverses direction.
3. A coil of 200 turns has its magnetic flux changed by 0.02 Wb in 0.5 s. Find the induced emf.
ε = N ΔΦ/Δt = 200 × 0.02 ÷ 0.5 = 8 V.
4. A transformer has 1000 turns on its primary and 50 turns on its secondary. The primary gets 230 V. What is the secondary voltage?
Vs = Vp × Ns/Np = 230 × 50/1000 = 11.5 V. It is a step-down transformer, like the one in a phone charger.
5. A vertical wire carries current upwards. Which way does the compass needle's field go round it, seen from above?
Point the right thumb up (current). The fingers curl anticlockwise when seen from above, so the field goes anticlockwise. This matches the needles in the 3D when the current is positive.
Common mistakes
- Thinking a charged object has "made" charge. Rubbing only moves electrons from one object to the other; total charge stays the same.
- Saying that opposite poles repel. Like poles repel; unlike poles attract.
- Expecting a current from a magnet that is at rest inside a coil. Induction needs a CHANGE in the field (movement).
- Using the right-hand grip rule for the force on a wire. The force direction uses Fleming's left-hand rule.