Charge and Its Properties

Two kinds of charge

Rub a glass rod with silk and hang it from a thread. Rub a second glass rod the same way and bring it near: the two rods push each other away. A plastic comb rubbed in dry hair behaves differently. It pulls the rubbed glass rod towards itself. So rubbing gives bodies a property that comes in two kinds. This property is electric charge.

Benjamin Franklin named the two kinds positive and negative. The glass rubbed with silk is called positive; the comb rubbed in hair is negative. The names are only labels, but they are useful ones. Charges of the same kind repel each other, and charges of opposite kinds attract each other.

Rubbing moves electrons

Every atom holds negative electrons around a positive nucleus, and a whole atom carries no net charge. When two different materials are rubbed together, some electrons cross from one surface to the other. The body that gains electrons becomes negative. The body that loses them is left positive by the same amount. Glass gives electrons to silk, and hair gives electrons to a plastic comb.

Conductors and insulators

In a metal, some electrons are not tied to any one atom. They drift freely through the whole piece. A material in which charge moves freely is a conductor: metals, the human body, the earth and tap water are conductors. In glass, plastic, rubber and dry air, every electron stays with its own atom. Such a material is an insulator. Charge placed on an insulator stays where it was put.

This is why the sweater crackles in winter and not in the monsoon. Humid air carries a thin film of water on every surface, and the charge leaks away through it. Dry winter air is a good insulator, so the charge stays on the sweater and builds up.

Charging by contact and by induction

Touch a charged metal ball to a neutral one, and some charge flows across, because metal lets it move. Both balls end with charge of the same sign. This is charging by contact. There is a second way that needs no touching at all. It uses the free electrons of a conductor, and it gives the conductor the opposite sign.

Follow Fig 1.1 step by step. The negative rod repels the free electrons of the sphere, so they crowd on the far side. The near side is left positive. This separation of charge is induction, and so far the sphere's total charge is still zero. Now connect the sphere to the ground by a wire. This is earthing: the earth is so large that it can take or give any amount of charge. The repelled electrons flow into it.

Remove the earth wire while the rod is still near. The electrons that left cannot come back, so the sphere now has a net positive charge. Finally take the rod away. The positive charge, no longer pulled to one side, spreads evenly over the surface. Induction always leaves a conductor with charge opposite to that of the body used.

Why neutral paper jumps to a comb

A bit of paper is an insulator, so its electrons cannot run to one side. Yet each molecule stretches a little in the comb's pull. The positive parts shift slightly towards the negative comb and the negative parts slightly away. This slight shift inside each molecule is called polarisation. The near face of the paper becomes a little positive and the far face a little negative.

The comb attracts the near face and repels the far face. The near face is closer, and the electric force weakens with distance, as the next lesson shows. So the attraction wins, and the neutral paper jumps to the comb. The sweater clings for a simpler reason. Rubbing on your shirt left the two with opposite charges, and opposite charges attract. The crackle is the charge jumping across the air in tiny sparks, as lesson 4 explains.

The gold-leaf electroscope

A gold-leaf electroscope shows whether a body is charged. A metal rod passes through an insulating stopper into a glass jar. At its lower end hang two thin leaves of gold foil. Touch a charged body to the metal cap on top, and charge spreads down to both leaves. The leaves carry like charge, so they repel and spread apart. The more charge, the wider they open.

A charged electroscope also tells the sign of a charge. Suppose its leaves carry negative charge. Bring a negative rod near the cap and more electrons are pushed down, so the leaves open further. Bring a positive rod near and electrons are pulled up, so the leaves fall together.

Charge comes in whole electrons

The SI unit of charge is the coulomb, C. The charge of one proton is \(+e\), and the charge of one electron is \(-e\), where \(e = 1.6 \times 10^{-19}\,\text{C}\). This smallest free charge is the elementary charge. Since charging moves whole electrons, a body can gain or lose only a whole number of them. Its charge is always a whole-number multiple of \(e\).

The numbers are huge because \(e\) is tiny. One coulomb is the charge of \(1/e = 6.25 \times 10^{18}\) electrons. Even a nanocoulomb, \(10^{-9}\,\text{C}\), is more than six billion electrons. So on everyday bodies the steps of \(e\) are far too small to notice, and charge behaves as if it could take any value.

Charge is never made or destroyed

When glass is rubbed with silk, the glass gains a positive charge and the silk an equal negative charge. The total before was zero, and the total after is still zero. In induction too the earth takes exactly the charge the sphere loses. In every process ever measured, charge only moves. This is the conservation of charge.

"Algebraic sum" means the signs count. A body with \(+5\,\mu\text{C}\) and another with \(-2\,\mu\text{C}\) hold a total of \(+3\,\mu\text{C}\). Charges add like signed numbers, and the total of an isolated system is what never changes.

Why equal shares in Fig 1.2? The two spheres are identical, and charge flows between them until neither is favoured over the other. So each ends with half the total: \((6 - 2)/2 = 2\,\mu\text{C}\). For two spheres of different sizes the shares are not equal, and the chapter on Conductors in Electrostatics finds them.