Electric Fields and Field Strength Revision Notes | A Level AQA Physics

1. Why Electric Fields Matter

Charged particles exert forces on each other across empty space. That seems strange — how can one object push or pull another without touching it? The answer lies in the concept of an electric field.

Think back to gravitational fields from earlier in the course. A mass creates a gravitational field around it, and any other mass placed in that field experiences a force. Electric fields work on exactly the same principle — but for charge rather than mass. A charged object creates an electric field in the space around it, and any other charged object placed in that field experiences a force.

This idea underpins everything from the behaviour of electrons in circuits to the operation of particle accelerators. Mastering electric fields now also sets you up for Coulomb's law and capacitors later in the course.

2. Representing Electric Fields with Field Lines

You cannot see an electric field, so physicists represent it using electric field lines — directed lines drawn in the space around a charge. Each line shows the direction of the force that a small positive test charge would experience if placed at that point.

There are two conventions you must know cold for the exam. First, field lines always point away from positive charges and towards negative charges — they show the direction of force on a positive test charge. Second, the closer together the lines are, the stronger the field at that region.

• Isolated positive charge: lines radiate outward in all directions, equally spaced, getting further apart with distance — showing the field weakens with distance.
• Isolated negative charge: lines point inward from all directions towards the charge.
• Two equal and opposite charges (electric dipole): lines leave the positive charge and curve round to enter the negative charge.
• Two parallel plates (uniform field): lines are straight, parallel, and equally spaced between the plates — field strength is constant throughout.

The parallel-plate case is particularly important. Between two oppositely charged plates, the field lines are uniform — they do not spread out or converge. This means the force on a charge placed anywhere between the plates is the same magnitude and direction, which makes calculations much more tractable.

3. Electric Field Strength: Defining the Quantity

Field lines give a qualitative picture, but physics demands numbers. To quantify how strong an electric field is at a particular point, we use the concept of electric field strength, given the symbol $E$.

Here is the key idea: imagine placing a very small positive charge — called a test charge — at the point of interest. The field exerts a force on that test charge. Electric field strength is defined as the ratio of that force to the size of the test charge. In other words, it tells you how many newtons of force act per coulomb of charge placed at that point.

Notice the phrase unit positive charge in the definition. The test charge must be positive by convention, because field lines are defined in terms of the force on a positive charge. If you placed a negative charge at the same point, the force would be in the opposite direction — but the field itself has not changed.

The equation rearranges in two useful ways. To find the force on a charge in a known field: $F = EQ$. To find the charge when you know the force and the field: $Q = \frac{F}{E}$. In the exam, you will need all three forms, so practise rearranging before you substitute numbers.

4. Worked Calculations Using $E = F/Q$

The equation $E = \frac{F}{Q}$ looks straightforward, but exam questions are designed to catch students who rush the substitution or forget to check units. Work through the following examples carefully — the method here is exactly what earns method marks.

Worked example: Calculating electric field strength from force and charge

A charge of $4.0 \times 10^{-6}$ C experiences a force of $2.0 \times 10^{-2}$ N when placed at a point in an electric field. Calculate the electric field strength at that point. [3 marks]

1. $E = \frac{F}{Q}$ — [M1] Stating the correct equation earns the first method mark.
2. $F = 2.0 \times 10^{-2}$ N, $\quad Q = 4.0 \times 10^{-6}$ C — Both values are already in SI base units (N and C), so no conversion is needed.
3. $E = \frac{2.0 \times 10^{-2}}{4.0 \times 10^{-6}}$ — [M1] Correct substitution with values and units.
4. $E = \frac{2.0}{4.0} \times \frac{10^{-2}}{10^{-6}} = 0.5 \times 10^{4} = 5.0 \times 10^{3}$ N C⁻¹ — Divide the coefficients: $2.0 \div 4.0 = 0.5$. Divide the powers: $10^{-2} \div 10^{-6} = 10^{-2-(-6)} = 10^{4}$. Combine: $0.5 \times 10^{4} = 5.0 \times 10^{3}$.
5. $E = 5.0 \times 10^{3}$ N C⁻¹ — [A1] Correct answer with correct unit. Always write N C⁻¹ (or equivalently V m⁻¹, though N C⁻¹ is the direct unit from this definition).

Answer: $E = 5.0 \times 10^{3}$ N C⁻¹

Now consider the reverse: you know the field strength and the charge, and you need the force. This is the $F = EQ$ rearrangement, and it comes up frequently in questions about charged particles moving through fields.

Worked example: Finding the force on a charge in a known field

An electric field has a field strength of $3.0 \times 10^{4}$ N C⁻¹. Calculate the force acting on a proton placed in this field. (Charge of a proton: $e = 1.6 \times 10^{-19}$ C) [3 marks]

1. $F = EQ$ — [M1] Rearranging $E = F/Q$ to make $F$ the subject.
2. $E = 3.0 \times 10^{4}$ N C⁻¹, $\quad Q = 1.6 \times 10^{-19}$ C — The charge on a proton equals the elementary charge $e$. This value is given in the AQA data booklet.
3. $F = 3.0 \times 10^{4} \times 1.6 \times 10^{-19}$ — [M1] Correct substitution.
4. $F = (3.0 \times 1.6) \times (10^{4} \times 10^{-19}) = 4.8 \times 10^{-15}$ N — Multiply coefficients: $3.0 \times 1.6 = 4.8$. Add exponents: $4 + (-19) = -15$.
5. $F = 4.8 \times 10^{-15}$ N — [A1] Correct answer with unit. The force is in the direction of the field because the proton carries positive charge.

Answer: $F = 4.8 \times 10^{-15}$ N

5. Uniform and Non-Uniform Fields: Reading the Diagram

Earlier you saw that field line spacing encodes field strength. This becomes a genuine analytical skill in the exam, where you may be given a field line diagram and asked to compare field strengths at different points or to describe how the field changes.

For a uniform field — such as between two large parallel plates — the lines are straight, parallel, and evenly spaced. The field strength $E$ is the same at every point between the plates. This is the simplest case and the one most commonly used in calculations at this level.

For a non-uniform field — such as around a point charge — the lines curve and their spacing changes. Where lines are close together, $E$ is large; where they spread apart, $E$ is small. Around a positive point charge, the field is strongest nearest the charge and decreases with distance.

The chart above illustrates how field strength falls off rapidly with distance from a point charge. At A-level you are not yet required to derive the exact relationship (that comes with Coulomb's law), but you must be able to describe and explain the trend using field line diagrams.

6. Connecting Field Lines to Field Strength: The Full Picture

You now have two complementary tools: field line diagrams (qualitative) and the equation $E = F/Q$ (quantitative). In the exam, questions often ask you to use both together — for example, to explain why the force on a charge changes as it moves through a non-uniform field.

Here is how the two tools connect. If a charge $Q$ moves from a region where lines are widely spaced (small $E$) to a region where lines are closely packed (large $E$), the force $F = EQ$ on the charge increases. The charge itself has not changed — only the field strength at its new location has changed.

This reasoning chain — field line spacing → field strength → force on charge — is exactly the kind of multi-step explanation that earns marks on 'explain' questions. Practise writing it out in full, using the equation to support your argument.

7. Exam Technique and Common Mistakes

Electric fields questions are reliable mark-scorers if you apply the right habits. The following guidance is drawn directly from the patterns that distinguish full-mark responses from partial-mark ones.

To consolidate everything, here is a summary of the three specification requirements and how they connect. Electric field lines represent the direction and relative strength of a field (requirement 1). Electric field strength $E$ is the quantitative measure of that field at a point (requirement 2). The defining equation $E = F/Q$ links field strength to the measurable force on a known charge, making the concept experimentally grounded and calculable (requirement 3).