Electric Charges and Fields

Lesson

Part 1 — what charge is, how charges push and pull, and how the idea of a field describes that push and pull at every point in space.

In this lesson you will

State the basic properties of electric charge and explain charging by induction
Apply Coulomb’s law in vector form and the principle of superposition
Calculate the electric field of a point charge and of a system of charges
Sketch and interpret electric field-line patterns

Concept

Properties of electric charge

Charge is a basic property of matter, measured in coulombs (C). Four properties matter for every problem in this chapter.

Table of the four basic properties of charge: two kinds, additivity, conservation and quantisation, with an example of each
Property	What it means	Example
Two kinds	Positive and negative; like repel, unlike attract	Glass rubbed with silk is positive; the silk is negative
Additivity	Total charge is the algebraic sum	$+3\,\mu\text{C}$ , $-5\,\mu\text{C}$ and $+1\,\mu\text{C}$ give $-1\,\mu\text{C}$
Conservation	Charge is neither created nor destroyed in an isolated system	Rubbing only transfers electrons
Quantisation	$q = n e$ , with $n$ an integer and $e = 1.6 \times 10^{-19}$ C	No body carries $0.8 \times 10^{-19}$ C

Concept

Quantisation in practice

Since $q = n e$ , the number of electrons transferred is $n = q/e$ . A body charged to $-1.0\,\mu\text{C}$ has gained $n = \dfrac{1.0 \times 10^{-6}}{1.6 \times 10^{-19}} = 6.25 \times 10^{12}$ extra electrons.

Everyday charges are huge multiples of $e$ , so charge looks continuous at the large scale.
A positively charged body has lost electrons; its mass decreases very slightly.
Quantisation matters at the atomic scale, for example in Millikan-style oil-drop experiments.

Table of three charges and the number of electrons gained or lost: minus one microcoulomb is six point two five times ten to the twelve electrons gained
Charge on body	Electrons gained or lost
$-1.0\,\mu\text{C}$	$6.25 \times 10^{12}$ gained
$+3.2 \times 10^{-18}$ C	20 lost
$+1.6 \times 10^{-19}$ C	1 lost

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