Charging and Conservation of Charge

Charge and the atom

Everything is made of atoms. An atom has a nucleus containing positive protons and neutral neutrons, surrounded by negative electrons. A neutral object has equal numbers of protons and electrons, so its net charge is zero.

The protons are locked in the nuclei and do not move when you charge something. Only electrons are transferred. The charge of one electron is $e = 1.602\times10^{-19}\ \text{C}$, and this is the smallest amount of free charge we meet. Every charge is a whole number of these:

where $n$ is the number of electrons gained or lost.

• An object that gains electrons has an excess of negative charge: it is negatively charged.

• An object that loses electrons has a deficit of electrons: it is positively charged.

The forces are simple: like charges repel, unlike charges attract, and a charged object also attracts a neutral one (we will see why in the section on induction).

Conductors and insulators

In a conductor, some electrons are not bound to any one atom. These free electrons can move through the whole material. Metals such as copper and aluminium are good conductors, and so is graphite.

In an insulator, all the electrons are bound electrons: they are tightly held by their atoms and cannot move far. In a conductor, the free electrons are the ones that carry charge, while the inner electrons stay bound. Polythene, glass, dry wood and rubber are insulators.

This matters when charging. Charge placed on an insulator stays where it is put. Charge placed on a conductor spreads out, and flows away if the conductor is connected to the earth. That is why we mount metal spheres on insulating stands.

Charging by friction and contact, and conservation of charge

Friction. When a polythene rod is rubbed with a woollen cloth, electrons are pulled off the wool and onto the polythene. The rod gains electrons and becomes negative. The cloth loses the same number and becomes positive. Nothing is created: charge is only moved from one object to the other.

Contact. When a charged conductor touches another conductor, charge flows between them until they share it. If two identical spheres touch, they end up with equal charges.

This all follows from the principle of conservation of charge:

Charging by induction and the electroscope

Induction charges an object without touching it with the charged object.

To charge a sphere positively using a negative rod:

1. Bring the negative rod close to the sphere (no touching). Electrons in the sphere are repelled to the far side. The near side is positive.

2. With the rod still there, connect the sphere to the earth with a wire or a finger. Electrons flow from the sphere to the earth, away from the repelling rod.

3. Remove the earth connection first, with the rod still in place. The sphere is now trapped with a deficit of electrons.

4. Remove the rod. The remaining positive charge spreads over the sphere.

The rod loses no charge because it never touches the sphere. The sphere ends up with the opposite sign to the rod, because the electrons that left were the ones repelled by it.

This also explains why a charged rod attracts a neutral object: the near side is given the opposite charge and the far side the same charge, but the near side is closer, so attraction wins.

The gold-leaf electroscope

A gold-leaf electroscope has a metal cap, a rod and a thin gold leaf hanging from a metal plate. Charge on the leaf and plate makes them repel, so the leaf rises. The more charge, the greater the rise.

To charge the electroscope, use the same four steps as for the sphere, with the finger acting as the earth. A charged electroscope can then test the sign of another charge: if the leaf rises further, the new charge has the same sign as the electroscope. If the leaf falls, the sign is opposite. Only a fall is a reliable test, because an object with the opposite charge brought close can first make the leaf fall and then, as it comes closer still, make it rise again by inducing the opposite charge on the leaf.

Charge on conductors, earthing and its uses

Where the charge sits. Excess charge on a conductor repels itself, so it moves as far apart as it can: to the outer surface. A hollow metal sphere and a solid one hold their excess charge in the same place. Inside, there is none.

Sharp points. On a conductor with a pointed part, the charge is more concentrated at the sharp point. The field there is strongest and can pull charge off into the air.

Insulators and induction. An insulator cannot let charge move through it, but its atoms can be polarised. When a charged rod comes near a neutral insulator, the electrons in each atom shift slightly away from (or towards) the rod. The near surface gets a small charge opposite to the rod and the far surface the same sign. The near side is closer, so the insulator is attracted, for example a scrap of paper jumping to a rubbed rod.

Earthing. The earth is a huge conductor that can supply or take up electrons without any noticeable change in its own charge. Connecting a charged object to it lets the excess charge flow away: electrons flow from the earth to a positive object, or from a negative object to the earth.

A real example. Fuel flowing through a pipe rubs against it, which can build up charge on a tanker. A spark could ignite petrol vapour. An earth wire lets electrons flow away continuously, so the tanker never reaches a high charge. A positive tanker is neutralised by electrons flowing from the earth to the tanker. A conducting nozzle also helps, as an insulating one would let charge build up on it.

Back to the start: when you walk on a carpet, friction transfers electrons between your shoes and the carpet, and your body becomes charged. Touching a metal handle gives the excess charge a path to the earth, so electrons flow in a tiny spark.

Summary