PhysicsCore18 min read

Electrostatics

Charges at rest, and the fields they create

This topic appears in:

10th Class Physics · ch.151st Year Physics · ch.92nd Year Physics · ch.12A Level Physics (9702) · ch.18
01

Charge, and how objects acquire it

Definition

Electric charge — A property of matter that causes it to experience a force in an electric field. It exists in two kinds, positive and negative, and is measured in coulombs.

Like charges repel and unlike charges attract. Everything in this topic follows from that one rule together with the fact that only electrons move.

Rub a polythene rod with a cloth and electrons are transferred from the cloth onto the rod. The rod, having gained electrons, becomes negative; the cloth, having lost them, becomes positive. Nothing is created — charge has simply been moved, which is the principle of conservation of charge.

This is why an object never becomes positive by gaining protons. Protons sit inside nuclei that are locked into the structure of the material and cannot go anywhere. Writing that "positive charge moved to the cloth" describes the right outcome by the wrong mechanism, and mark schemes do not accept it.

Charge is also quantised: every charge that can be measured is a whole-number multiple of the elementary charge e = 1.6 × 10⁻¹⁹ C. There is no such thing as half an electron of charge.

Q = n ee = 1.6 × 10⁻¹⁹ Cn is a whole number — charge comes in indivisible steps
Q
chargeC
n
number of elementary charges
e
elementary chargeC
02

Induced charge and why a charged rod attracts paper

A charged rod attracts small pieces of paper even though the paper is uncharged overall. This looks like a contradiction of the like-repels-unlike-attracts rule, and explaining it properly is a standard exam question.

Bringing a negative rod close to the paper pushes the paper's own electrons to the far side. The near side is left with a net positive charge and the far side with a net negative charge. The paper as a whole is still neutral — the charge has only been separated, not added.

Now both forces act: attraction between the rod and the near positive side, repulsion between the rod and the far negative side. They are not equal, because the near side is closer, and electrostatic force falls off sharply with distance. Attraction wins, and the paper jumps to the rod.

The distance argument is essential. Without it the two forces would cancel exactly and nothing would move — so an answer that omits it has not actually explained anything.

Earthing

Connecting a charged conductor to earth gives its excess charge a conducting path away, and the object returns to neutral. This is why fuel tankers are earthed before transfer and why you touch a metal pipe before handling sensitive components — the charge leaks away steadily instead of building up to a spark.

03

Coulomb's law

The force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This is Coulomb's law, and its form is deliberately familiar: it is the same inverse-square shape as Newton's law of gravitation.

The inverse square is worth pausing on. Double the separation and the force falls to a quarter, not a half. Treble it and the force falls to a ninth. Questions test this constantly by changing the distance and asking for the new force.

There is one important difference from gravity. Gravity only ever attracts, because there is only one kind of mass. Electrostatic force can attract or repel, because there are two kinds of charge — which is why electric field lines have a direction and gravitational ones always point inwards.

F = k q₁q₂ / r²k = 1/(4πε₀) ≈ 9 × 10⁹ N m² C⁻²inverse square — doubling r divides the force by four
F
forceN
q
chargeC
r
separationm
k
Coulomb constantN m² C⁻²
Worked example 15 marks

Two charges of +3.0 × 10⁻⁶ C and −2.0 × 10⁻⁶ C are 0.20 m apart. Calculate the force between them, and state what it becomes if the separation is doubled.

  1. Use F = k q₁q₂ / r².
  2. F = 9 × 10⁹ × (3.0 × 10⁻⁶ × 2.0 × 10⁻⁶) / 0.20².Use the magnitudes; decide attraction or repulsion separately from the signs.
  3. Numerator = 9 × 10⁹ × 6.0 × 10⁻¹² = 5.4 × 10⁻².
  4. F = 5.4 × 10⁻² / 0.040 = 1.35 N, attractive.The charges are unlike, so they attract.
  5. Doubling r divides the force by four: 0.34 N.Inverse square, not inverse.

1.35 N attractive; 0.34 N at double the separation

04

Electric fields

Definition

Electric field strength — The force per unit positive charge at a point in the field, E = F/q. Measured in newtons per coulomb, or equivalently volts per metre.

Rather than asking about the force between two particular charges, it is far more useful to describe the field that one charge creates — the condition it establishes in the space around it, which any other charge placed there will respond to.

Field lines show the direction of the force on a small positive test charge. That word "positive" is the whole convention, and it is what makes the direction well defined. Lines run outward from a positive charge and inward to a negative one, they never cross, and where they crowd together the field is strong.

A negative charge placed in the field therefore feels a force opposite to the field direction. Students lose marks on this constantly: field direction is defined for a positive charge, so a negative charge always goes the other way.

Between two parallel charged plates the field is uniform — the lines are parallel and evenly spaced, and the field strength is the same everywhere between them, away from the edges.

E = F / qE = k Q / r²E = V / d(uniform field)the last form is for parallel plates, where d is the plate separation in metres
E
field strengthN C⁻¹ or V m⁻¹
V
potential differenceV
d
plate separationm

Field lines leave positive charges and land on negative ones, and never cross. Set two like charges and a null point appears exactly midway, where the two fields cancel — put a charge there and it feels no force at all.

05

Potential, and everyday electrostatics

Electric potential is the energy per unit charge at a point in the field. It is a scalar, which makes it far easier to handle than field strength: potentials from several charges are added as ordinary numbers, with no directions to resolve.

A potential difference between two points is what drives charge from one to the other. This connects electrostatics directly to circuit work — the volt in a circuit is the same volt as here, one joule per coulomb.

The effects show up everywhere once you look. Lightning is the discharge of an enormous potential difference built up between cloud and ground. A photocopier charges a drum so that toner sticks only where the image is dark. Electrostatic precipitators charge smoke particles so they can be collected on plates instead of leaving a chimney. Spray painting charges the droplets so they are attracted evenly onto the object, wasting far less paint.

The hazards are the same effect uncontrolled. Charge accumulating on a fuel tanker or a grain silo can spark and ignite vapour or dust — which is why both are earthed before any transfer begins.

Key points

  1. Only electrons move; charge is conserved and quantised in units of 1.6 × 10⁻¹⁹ C.
  2. Induced charge separation explains why a charged rod attracts neutral paper — the near side is closer.
  3. Coulomb's law is inverse square: double the distance, quarter the force.
  4. Field lines run from positive to negative and show the force on a positive charge.
  5. Between parallel plates the field is uniform and E = V/d.

Practice questions

6 questions · 24 marks · full working on every one

Try each one on paper first, then open the working. The marks are shown where they are actually awarded, because that is where they are actually lost.

Short questions

3 · 6 marks

Two marks each, in the style of the short-question section of the paper. Answer in two or three lines.

SQ1[2 marks]
Explain, in terms of electrons, how a polythene rod becomes negatively charged when rubbed with a cloth.
Model answer

Electrons are transferred from the cloth onto the rod. The rod gains electrons and becomes negative; the cloth is left with a positive charge.

Examiner tip. Only electrons move. Saying "positive charge moves to the cloth" scores nothing.

SQ2[2 marks]
State what is meant by an electric field and how its direction is defined.
Model answer

A region in which a charge experiences a force. The direction of the field is the direction of the force on a small positive test charge.

Examiner tip. The word "positive" in the second half is the mark.

SQ3[2 marks]
Explain why a charged rod attracts small uncharged pieces of paper.
Model answer

The rod induces a separation of charge in the paper, drawing the opposite charge to the near side. That near charge is closer to the rod, so its attraction outweighs the repulsion of the far side.

Examiner tip. The distance argument is essential. Without it the two forces would cancel and nothing would move.

Solved numericals

1 · 4 marks

Full working, one step per line, with the marks shown where they are awarded.

N1[4 marks]
A potential difference of 5000 V is applied across two parallel plates separated by 25 mm. Calculate the electric field strength between them, and the force on a charge of 3.2 × 10⁻¹⁹ C placed in that field.
Full working
  1. Converts 25 mm = 0.025 m[1]
  2. Uses E = V/d = 5000 / 0.025[1]
  3. E = 2.0 × 10⁵ V m⁻¹[1]
  4. F = QE = 3.2 × 10⁻¹⁹ × 2.0 × 10⁵ = 6.4 × 10⁻¹⁴ N[1]

E = 2.0 × 10⁵ V m⁻¹, F = 6.4 × 10⁻¹⁴ N

Examiner tip. Volts per metre requires the separation in metres. Leaving it in millimetres is the classic slip here.

Long questions

1 · 8 marks

Theory and numerical together, as they appear in the long-question section.

LQ1[8 marks]
A fuel tanker is fitted with a conducting strip that touches the ground, and is earthed with a metal wire before fuel is transferred.
  1. Explain how charge builds up on the tanker as it drives. [2]
  2. Explain why this build-up is dangerous during refuelling. [3]
  3. Explain how earthing the tanker removes the danger. [3]
Mark scheme
  1. Friction between the tanker and the air, and between the fuel and the tank walls, transfers electrons[1]
  2. The tanker is insulated by its rubber tyres, so the charge cannot escape and accumulates[1]
  3. The charge raises the potential of the tanker[1]
  4. Eventually a spark jumps to a nearby earthed object[1]
  5. The spark could ignite the fuel vapour and cause an explosion[1]
  6. The wire provides a conducting path to earth[1]
  7. Electrons flow along it until the tanker is at the same potential as the earth[1]
  8. So charge leaks away steadily instead of building to a spark[1]

Examiner tip. Every earthing question follows the same three steps: charge builds because it cannot escape, a spark follows, the wire lets it drain away safely. Learn the sequence once and it answers all of them.

Exam questions

1 · 6 marks

Multi-part questions with a full mark scheme.

Q1[6 marks]
Two parallel metal plates are connected to a high-voltage supply, the upper plate positive.
  1. Describe the pattern of the field lines between the plates, away from the edges. [2]
  2. A small negatively charged oil drop is placed between the plates. State the direction of the electric force on it and explain your answer. [2]
  3. State two changes that would increase the force on the drop. [2]
Mark scheme
  1. The lines are parallel and equally spaced, showing a uniform field[1]
  2. They run from the positive plate to the negative plate[1]
  3. The force is upward, towards the positive plate[1]
  4. Because the drop is negative, so the force is opposite to the field direction[1]
  5. Increase the potential difference across the plates[1]
  6. Move the plates closer together, or increase the charge on the dropany one[1]

(b) upward, towards the positive plate

Examiner tip. Field direction is defined for a positive charge, so a negative charge always feels a force the other way. Write that sentence down — it is the explanation mark.