Electrostatics

Rub a balloon on your hair and it will stick to the wall; drag a plastic comb through dry hair and it lifts tiny bits of paper. Both show static electricity — electric charge that sits still on a surface. Rubbing does not make charge; it simply transfers electrons from one body to the other. The balloon steals electrons and becomes negative; your hair loses them and becomes positive.

• Two kinds of charge — positive (electron-deficient) and negative (electron-excess). The proton is +e, the electron is −e.
• The rule of force — like charges repel, unlike charges attract. Two negative balloons push apart; the negative balloon and the positive wall pull together.
• Conservation of charge — charge is never created or destroyed, only moved. The hair gains exactly the positive charge the balloon gains as negative.
• Quantisation of charge — charge comes in whole multiples of the electron's charge: q = ± n e, where e = 1.6 × 10⁻¹⁹ C. You can never have half an electron's worth.

Touch one end of a metal rod with a charged object and the charge races along the whole rod in an instant — metals have free electrons that wander through them. Do the same to a plastic comb and the charge just sits where you put it; plastic has no free electrons to carry it.

• Conductor — a material with free (mobile) electrons: metals, the human body, salty water. Charge moves easily and spreads over the whole outer surface.
• Insulator (dielectric) — a material with no free charges: plastic, glass, rubber, dry wood. Charge stays trapped where it is deposited.
• Earthing (grounding) — connecting a charged conductor to the ground by a wire lets the excess charge flow away into the huge reservoir of the Earth, making the body neutral and safe.

Hang two small charged spheres side by side and they push apart. Coulomb measured exactly how hard: the force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.

1. Double a charge → double the force. Triple both charges → nine times the force.
2. Inverse square: halve the distance → the force becomes four times bigger. Triple the distance → one-ninth.
3. The force acts along the line joining the charges; repulsive for like, attractive for unlike (Newton's third law — equal and opposite).
4. In a medium of permittivity ε, divide by the relative permittivity εᵣ — water (εᵣ ≈ 80) weakens the force eightyfold.

How does one charge "know" the other is there without touching? Each charge fills the space around itself with an electric field — a region where any other charge feels a force. Bring a tiny positive test charge near a source charge and it is pushed outward; the field strength is the force felt per unit charge.

1. E = F/q — the force a unit positive charge would feel; its direction is the direction of that force.
2. The field points away from a positive charge and towards a negative charge.
3. For a point charge the field also obeys the inverse-square law: E = kQ/r², fading fast as you move away.
4. Once E is known, the force on any charge placed there is simply F = qE.

We draw the invisible field as field lines — like iron filings tracing a magnet, they make the field visible. A line shows the direction a free positive charge would move, and where the lines crowd together the field is stronger.

1. Field lines begin on positive charge and end on negative charge; they never form closed loops.
2. Two field lines never cross — the field has only one direction at each point.
3. Between charged parallel plates the lines are parallel and equally spaced, so the field E = V/d is the same everywhere — this uniform field is the key to capacitors.

Pushing a positive charge towards another positive charge is exactly like carrying a ball up a hill — you must do work against a force, and that work is stored. The higher up the hill (the closer to the charge), the higher the electric potential. Potential is the potential energy per unit charge at a point.

1. Potential difference (p.d.) between two points is the work done per unit charge to move a charge between them: V = W/q.
2. One volt = one joule of work per coulomb of charge moved.
3. Positive charges move from high to low potential by themselves (downhill); pushing them uphill needs an external agent (a battery).
4. Unlike the field, potential is a scalar — no direction, just a number at each point. Points of equal potential form equipotential surfaces.

Put two parallel metal plates close together, connect them to a battery, and one plate fills with positive charge while the other fills with negative. The pair stores charge — it is a capacitor. Think of a bucket or reservoir: a wide bucket holds far more water for the same depth, just as a big capacitor holds more charge for the same voltage.

1. Capacitance C measures how much charge a body stores per volt — the "size of the bucket".
2. Q = CV: for a fixed capacitor, more voltage pushes in proportionally more charge.
3. The farad is huge, so real capacitors are rated in microfarads (μF), nanofarads or picofarads.
4. Bigger plate area and a smaller gap → larger capacitance. (The full formula comes in Chapter 2.)

Every idea in this chapter shows up in machines and nature around you:

• Lightning — friction between rising and falling ice in a storm cloud separates huge charge until the field breaks down the air and a giant spark (the discharge) leaps to earth.
• Van de Graaff generator — a moving belt carries charge up to a metal dome, building it to hundreds of thousands of volts; touch it and your hair stands on end as like charges repel.
• Photocopier & laser printer — a charged drum holds an image in static charge; oppositely-charged toner powder is attracted onto it, then pressed and heated onto the paper.
• Faraday cage / shielding — charge sits only on the outside of a conductor, so the inside is field-free. That is why you are safe inside a car or aeroplane struck by lightning.

1. Charge: two kinds, like repels / unlike attracts, conserved and quantised (q = ne).
2. Conductors carry charge freely; insulators trap it; earthing drains it.
3. Coulomb's law: F = k q₁q₂ / r², inverse-square, k = 9 × 10⁹.
4. Field: E = F/q (N/C); for a point charge E = kQ/r².
5. Field lines: out of +, into −; uniform between parallel plates.
6. Potential: V = W/q (volts); V = kQ/r; a scalar.
7. Capacitance: Q = CV, measured in farads.