In Attraction and Repulsion you saw that like charges repel and unlike charges attract. Now we look at charge itself: where it comes from, how objects get it, and the two rules it always obeys.
Why it works
Ordinary matter is made of atoms: protons, each with charge $+e$, and electrons, each with $-e$, where $e = 1.60 \times 10^{-19}\,\text{C}$. A neutral object is not empty of charge; it holds equal numbers of both. Charging an object never creates charge: it moves electrons from one place to another. So the total charge never changes (conservation), and any object's net charge is a whole number of electrons' worth, $q = \pm Ne$ (quantization).
Key idea
Charge is conserved and comes in whole multiples of $e = 1.60 \times 10^{-19}\,\text{C}$. Objects charge by friction (rubbing moves electrons), by contact (a conductor shares charge), or by induction (a nearby charge pushes charges around, and a ground connection lets some leave or arrive).
- Conductors, such as metals, have electrons free to move through them, so charge spreads over them.
- Insulators, such as plastic and glass, hold their electrons in place, so charge stays where it is put.
- Two identical metal spheres that touch end up sharing their total charge equally.
Worked examples
Worked example: Counting electrons
A balloon rubbed on hair gains $5.0 \times 10^{11}$ electrons. What is its charge?
- Each electron carries $-1.60 \times 10^{-19}\,\text{C}$.
- $q = -(5.0 \times 10^{11})(1.60 \times 10^{-19}\,\text{C}) = -8.0 \times 10^{-8}\,\text{C} = -80\,\text{nC}$.
- The hair lost the same number of electrons, so it carries $+80\,\text{nC}$. The total is still zero.
Answer: $-8.0 \times 10^{-8}\,\text{C}$
Worked example: Sharing by contact
Two identical metal spheres carry $+6\,\text{nC}$ and $-2\,\text{nC}$. They touch and are pulled apart. What is the charge on each?
- Total charge: $6 + (-2) = +4\,\text{nC}$, which is conserved.
- Identical conductors share it equally: $+2\,\text{nC}$ each. (Electrons flowed from the negative sphere to the positive one.)
Answer: $+2\,\text{nC}$ each
Worked example: Charging by induction
A negative rod is held near a neutral metal sphere. You touch the sphere's far side with a grounded wire, remove the wire, then remove the rod. What charge does the sphere keep?
- The rod pushes the sphere's electrons to the far side.
- The ground wire gives those electrons a way out, and some leave.
- With the wire gone first, they cannot come back. The sphere is left short of electrons: positive, the opposite of the rod.
Answer: Positive
Common mistake
Thinking a neutral object holds no charges at all, so nothing could attract it. A neutral object has equal amounts of positive and negative charge, and they can shift. That is why a charged balloon picks up neutral bits of paper: the paper polarizes, and its near side, with the opposite charge, is attracted more strongly than its far side is repelled.