IMAT Physics · Electricity

Electric Charge, Conductors and Coulomb's Law

Charge comes in whole numbers of electron charges, is never created or destroyed, moves freely only in conductors, and pushes or pulls other charges with a force that falls as 1/r².

All Electricity notes

Why this matters

The 2019 paper asked how the force between two charges changes when the charges and the distance change. The 2023 and 2026 ministry papers asked plain facts: what happens to the charge when two insulating spheres touch, and the charge of a hydrogen atom.

Concept 1 of 4: Electric charge: carried by particles, quantised and conserved

Every atom holds positive protons in its nucleus and the same number of negative electrons around it, so a whole atom has no net charge. An object becomes charged only when electrons leave it or join it. Charge cannot appear from nothing: whatever one object gains, another object loses.

Definition

Electric charge is measured in coulombs (C).

The elementary charge is $e = 1.6 \times 10^{-19}\ \text{C}$ . A proton carries $+e$ , an electron $-e$ , a neutron $0$ .
Charge is quantised: any charge is a whole number of elementary charges, $Q = ne$ .
Charge is conserved: in any process the total charge stays the same. Rubbing a rod with a cloth moves electrons from one to the other; the rod and cloth end with equal and opposite charges.
A neutral atom (hydrogen, or any other) has a net charge of exactly zero. An ion has gained or lost electrons.
In solids only electrons move. A positive object has lost electrons; it has not gained protons.

Charge as a count of elementary charges

Q = n e

$Q$ charge, in C
$n$ number of electrons gained or lost (a whole number)
$e$ elementary charge, $1.6 \times 10^{-19}\ \text{C}$

Worked example

A plastic rod is rubbed with a wool cloth and gains

5.0 \times 10^{11}

electrons from it. What are the charges on the rod and on the cloth afterwards?

Practice this conceptself-check · 4 quick reps

A neutral atom has zero charge, not a small one

An atom has as many electrons as protons, so the charges cancel exactly. Its net charge is 0 C. Options giving a neutral atom a tiny charge in nC or pC are wrong; only an ion carries a net charge.

Positive charge means electrons lost, not protons gained

Protons are locked in nuclei and do not move from one solid to another. A body becomes positive by losing electrons and negative by gaining them.

Concept 2 of 4: Conductors and insulators: where charge can move

In a metal some electrons are not tied to any one atom, so they drift through the whole piece and carry charge with them. In an insulator every electron stays with its own atom, so a charge placed on it stays where it was put. That single difference decides what happens when charged objects touch.

Definition

A conductor has charges free to move (electrons in metals, ions in solutions). Extra charge on an isolated conductor spreads out until it sits on the outer surface.
An insulator has no free charges. Charge placed on it stays in place, and touching another body does not share it out.
When two identical metal spheres touch, they share the total charge equally. Total charge before = total charge after.
When two insulating bodies touch, each keeps (to a first approximation) its own charge.
Earthing a conductor connects it to the ground, which can give or take any number of electrons, so the conductor ends up neutral.

Material	Free charge carriers	Charge placed on it	Examples
Metal (conductor)	Electrons	Spreads over the outer surface	Copper, aluminium, gold
Electrolyte (conductor)	Positive and negative ions	Moves with the ions	Salt water, blood plasma, acid solutions
Semiconductor	A few electrons, more when warmer	Moves slowly	Silicon, germanium
Insulator	None	Stays where it was placed	Glass, plastic, rubber, dry air, pure water (nearly)

Most metals conduct better when cold; semiconductors conduct better when warm.

Practice this conceptself-check · 3 quick reps

Insulators do not share charge on contact

Sharing charge equally on contact is a property of conductors. If two insulating bodies touch, the charge cannot flow, so each keeps the charge it had. Options that average the charges by size or radius apply only to metals.

Concept 3 of 4: Coulomb's law: the force between two point charges

Like charges repel and unlike charges attract. The force grows with each charge and weakens quickly with distance: double the gap and the force drops to a quarter. Each charge pulls or pushes the other equally hard, even if one charge is much bigger.

Definition

Coulomb's law: two point charges $q_1$ and $q_2$ a distance $r$ apart exert equal and opposite forces on each other, along the line joining them.

The size is proportional to $q_1 q_2$ and to $1/r^2$ (an inverse square law).
$k = \dfrac{1}{4\pi\varepsilon_0} \approx 9.0 \times 10^9\ \text{N m}^2/\text{C}^2$ in a vacuum (or air).
Like signs repel, opposite signs attract.
For ratio questions, write the new force as a fraction of the old: multiply by each charge's factor and divide by the distance factor squared.

Coulomb's law

F = k\,\frac{q_1 q_2}{r^2}

$F$ force on each charge, in N
$q_1, q_2$ the two charges, in C
$r$ distance between them, in m
$k$ $9.0 \times 10^9\ \text{N m}^2/\text{C}^2$

Worked example

Charges of

+2.0\ \mu\text{C}

and

-3.0\ \mu\text{C}

are 0.30 m apart in air. Find the size of the force between them and say whether it attracts or repels.

Practice this conceptself-check · 3 quick reps

The bigger charge does not feel a bigger force

The forces on the two charges are a Newton's third law pair: equal in size and opposite in direction, whatever the two charges are. Only the accelerations can differ, because the masses can differ.

Distance enters squared

Coulomb's law is an inverse square law. Tripling the distance divides the force by 9, not by 3. Options that divide by the distance factor alone are the usual distractor.

Concept 4 of 4: Electric field: force per unit charge, and field lines

A charge changes the space around it, so that any other charge placed there feels a force. The electric field at a point is the force a +1 C test charge would feel there. Once you know the field, the force on any charge is just the charge times the field.

Definition

The electric field $E$ at a point is the force per unit positive charge placed there: $E = F/q$ , in N/C (the same as V/m).

Around a point charge $Q$ : $E = kQ/r^2$ , pointing away from a positive charge and towards a negative one.
A positive charge is pushed along the field; a negative charge (an electron) is pushed against it.
Field lines start on positive charges and end on negative ones. They never cross, and where they are closer together the field is stronger.
Between two parallel charged plates the lines are straight, parallel and evenly spaced: a uniform field.

Electric field

E = \frac{F}{q} \qquad E = k\,\frac{Q}{r^2}

$E$ electric field strength, in N/C
$F$ force on a charge $q$ placed in the field, in N
$Q$ the charge that makes the field, in C
$r$ distance from $Q$ , in m

Worked example

Find the electric field 0.20 m from a charge of

+4.0\ \text{nC}

. An electron is placed at that point: what force acts on it, and in which direction?

Practice this conceptself-check · 3 quick reps

Electrons move against the field

The field direction is defined by the force on a positive charge. An electron feels a force of the same size in the opposite direction. Options that send an electron along the field lines are wrong.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (3)

Electric charge: carried by particles, quantised and conserved
Charge as a count of elementary charges
$Q = n e$
Coulomb's law: the force between two point charges
Coulomb's law
$F = k\,\frac{q_1 q_2}{r^2}$
Electric field: force per unit charge, and field lines
Electric field
$E = \frac{F}{q} \qquad E = k\,\frac{Q}{r^2}$

Reference tables (1)

Conductors and insulators: where charge can move4 rows

Material	Free charge carriers	Charge placed on it	Examples
Metal (conductor)	Electrons	Spreads over the outer surface	Copper, aluminium, gold
Electrolyte (conductor)	Positive and negative ions	Moves with the ions	Salt water, blood plasma, acid solutions
Semiconductor	A few electrons, more when warmer	Moves slowly	Silicon, germanium
Insulator	None	Stays where it was placed	Glass, plastic, rubber, dry air, pure water (nearly)

Most metals conduct better when cold; semiconductors conduct better when warm.

Watch out for (6)

A neutral atom has zero charge, not a small one
→ Electric charge: carried by particles, quantised and conserved
Positive charge means electrons lost, not protons gained
→ Electric charge: carried by particles, quantised and conserved
Insulators do not share charge on contact
→ Conductors and insulators: where charge can move
The bigger charge does not feel a bigger force
→ Coulomb's law: the force between two point charges
Distance enters squared
→ Coulomb's law: the force between two point charges
Electrons move against the field
→ Electric field: force per unit charge, and field lines

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