Conservation of Electric Charge and the Process of Charging

Shuffle across a wool rug in rubber-soled shoes and touch a doorknob, and the spark you feel is electrons your soles scraped off the rug on the way. You came away negative, the rug positive, by exactly equal amounts. No charge was made: electrons moved from one object to the other, and the total stayed zero. That bookkeeping rule, charge conservation, together with the difference between conductors and insulators from topic 8.1, explains every way an object gets charged.

Charge is conserved

Pick a system: any object or collection of objects you choose to track, with everything else called its surroundings. The net charge of the system is the sum of the charges of everything in it, signs included.

In solids the charge that moves is almost always electrons. Protons are bound in nuclei, deep inside atoms, and stay put. So "an object became positive" means it lost electrons, and "it became negative" means it gained them. An object with charge $+q$ is missing $N = \frac{q}{e}$ electrons. (In liquids and gases whole ions can move, which is how charge flows through salt water or a spark, but the bookkeeping is the same.)

Conservation is not an approximation. In particle collisions, new charged particles do get created, but always in pairs whose charges sum to zero, such as an electron and a positron. No experiment has ever found the net charge of an isolated system changing.

Inside a system, charge can also rearrange without any crossing the boundary: the net charge stays the same while the charge distribution shifts, as it does whenever another charged object comes close (polarization, below).

Charging by friction and by contact

Friction. When two different materials touch, electrons at the contact points move from the material that holds them less tightly to the one that holds them more tightly. Rubbing makes many more contact points, so more electrons move. Rubber and plastic grab electrons from hair, wool and skin; glass rubbed with silk gives up electrons. The two objects end with charges that are equal in size and opposite in sign, because the electrons one lost are exactly the ones the other gained.

Contact. When a charged object touches a second object, some of its excess charge spreads onto the second. What happens next depends on the material.

• On a conductor, the transferred charge spreads over the whole object, because charge carriers move freely and like charges push each other apart.
• On an insulator, the charge stays near the spot where it landed. A plastic rod touched to a metal ball at one end gives up only the charge near its tip.

When two identical metal spheres touch, they end with equal charges: nothing distinguishes one sphere from the other, so the charge has no reason to prefer either. Each gets half the total. For example, spheres with $+9.0\ \text{nC}$ and $-3.0\ \text{nC}$ touch and separate with $+3.0\ \text{nC}$ each; the total, $+6.0\ \text{nC}$, is unchanged. (Topic 10.2 handles spheres of different sizes, which do not share equally.)

Polarization: charge separation without transfer

A charged object can rearrange the charge in a nearby object without touching it. Its electric force pulls opposite charge toward it and pushes like charge away inside the second object. This induced charge separation is polarization, and it happens even if the second object is neutral overall.

• In a conductor, free electrons move across the whole object. Bring a negative rod near one end of a neutral metal can and electrons flee to the far side, leaving the near side positive. The can's net charge is still zero.
• In an insulator, electrons can't leave their atoms, but each atom's or molecule's electron cloud shifts slightly away from the negative rod (topic 8.1). The surface facing the rod ends up slightly positive and the far surface slightly negative.

Polarization explains why a charged object attracts neutral ones: a comb attracts bits of paper, a balloon sticks to a wall. The induced charge opposite to the rod's sits closer to the rod than the induced like charge, and the Coulomb force weakens with distance, so the attraction wins. For example, if a $+10\ \text{nC}$ rod induces $-1.0\ \text{nC}$ on the near side of a neutral object $5.0\ \text{cm}$ away and $+1.0\ \text{nC}$ on its far side $5.4\ \text{cm}$ away, the attraction is $3.6\times10^{-5}\ \text{N}$ and the repulsion is $3.1\times10^{-5}\ \text{N}$, a net pull of $5\times10^{-6}\ \text{N}$ toward the rod. A neutral object is attracted by a positive rod and by a negative rod alike.

That has a consequence for experiments: attraction can't tell you that an object is charged, because a neutral object is attracted too. Repulsion can. If an object is repelled by a rod known to be negative, the object must be negative.

Grounding and charging by induction

Grounding means connecting an object by a conductor (a wire, a metal pipe, a person) to Earth. Earth is so large, and so close to neutral, that it can supply or absorb any amount of electrons an everyday object needs without its own charge changing noticeably. It is a charge reservoir.

A grounded conductor with no other charges nearby ends up neutral: excess electrons flow to Earth, or missing electrons flow up from it. This is why fuel trucks are grounded before they pump, and why electronics workers wear grounded wrist straps. With a charged object nearby, a grounded conductor ends up with a net charge, which gives a way to charge an object without touching it with anything charged.

Charging by induction, step by step, with a negative rod:

1. Hold the rod near a neutral metal sphere on an insulating stand. Electrons in the sphere are pushed to the far side; the near side is left positive.
2. Ground the sphere. Electrons, still repelled by the rod, now have somewhere farther to go: they flow down to Earth. It doesn't matter where on the sphere the ground wire touches, even the side nearest the rod; the whole sphere is one conductor.
3. Disconnect the ground while the rod is still near. The electrons that left can't come back.
4. Remove the rod. The sphere is missing electrons, so it is positive, and its charge spreads over its surface.

The sphere ends with the sign opposite to the rod's, and the rod loses none of its own charge. The order of steps 3 and 4 matters: remove the rod first, and the electrons flow back up from Earth through the wire, leaving the sphere neutral.

Worked examples

Where students lose points

On the exam

Questions on this topic ask you to predict the sign of an object's final charge after a sequence of steps, draw the charge distribution on a conductor or insulator (plus and minus signs placed where the charge sits), justify a claim in a few sentences, or convert between a charge and a number of electrons, as in Examples 1 to 3. A full justification names the mechanism (transfer of electrons, polarization, grounding) and cites conservation of charge where totals are involved.