# Electric field concepts

> CIE A-Level Physics · A2 Unit 21: Electric fields
> Source: https://www.owlsprep.com/study/cie-9702-u21-electric-field-concepts/

This sub-topic covers core definitions and visual representations of electric fields, the foundational concept for all A2 electrostatics topics including Coulomb's law, electric potential and capacitance.

**Prerequisites:** [AS Level charge and electric current](https://www.owlsprep.com/study/cie-9702-u10-charge-and-current/)

## Learning objectives

- Define electric field and electric field strength correctly
- Describe key properties of electric field lines
- Distinguish between uniform and radial electric fields
- Explain the requirement for a small test charge

## Core Definitions: Electric Field and Strength

An electric field describes the electrostatic influence a charged object has on other charges in the space around it. We quantify how strong the field is at any point using electric field strength.

**Electric field strength** — The force per unit positive charge acting on a very small test charge placed at the point.

*Notation:* $E = \frac{F}{Q}$

*Example:* If a 1 C charge experiences 10 N force, $E = 10 \, \text{N C}^{-1}$

**Worked example:** A test charge of $3.0 \times 10^{-6} \, \text{C}$ experiences an electrostatic force of $1.2 \times 10^{-2} \, \text{N}$ in an electric field. Calculate the electric field strength at that point.

1. Recall the definition of electric field strength:
2. $$E = \frac{F}{Q}$$
3. Substitute the given values: $F = 1.2 \times 10^{-2} \, \text{N}$, $Q = 3.0 \times 10^{-6} \, \text{C}$
4. $$E = \frac{1.2 \times 10^{-2}}{3.0 \times 10^{-6}} = 4000 \, \text{N C}^{-1}$$
5. This can also be written as $4000 \, \text{V m}^{-1}$, an equivalent unit accepted by CIE.

> **Exam tip:** CIE mark schemes accept both $\text{N C}^{-1}$ and $\text{V m}^{-1}$ as correct units for electric field strength, but always match units to the calculation context.

## Electric Field Lines

Field lines are a standard visual representation of electric fields that show both direction and relative strength of the field at any point.

**Electric field line rules** — Key rules for drawing electric field lines for CIE exams

1. The tangent to a field line at any point gives the direction of force on a small positive test charge at that point
2. The spacing between lines shows relative strength: closer lines = stronger field
3. Field lines never cross each other (two force directions at one point is impossible)
4. Field lines start on positive charges and end on negative charges (or infinity for isolated charges)

**Worked example:** Describe the electric field pattern around an isolated negative point charge.

1. Field lines are drawn radially, pointing inwards towards the negative point charge
2. Lines are more closely spaced near the charge, and get further apart as distance from the charge increases
3. All lines end on the negative charge, no lines cross, and strength decreases with distance from the charge

## Uniform vs Radial Electric Fields

CIE A-Level Physics most commonly tests two types of electric field: uniform and radial (non-uniform). Both have distinct properties and field line patterns.

| Property | Uniform Field | Radial Field |
| --- | --- | --- |
| Source | Between two oppositely charged parallel plates | Around a point charge/spherical charged object |
| Field strength | Constant everywhere (edge effects ignored) | Decreases with distance from source |
| Field line pattern | Parallel, equally spaced straight lines | Radial lines, spacing increases with distance |

**Worked example:** Compare the electric field strength between two oppositely charged parallel plates and around an isolated positive point charge.

1. Between the parallel plates, the electric field strength is uniform: it has the same magnitude and direction at all points between the plates (excluding edges)
2. Field lines are parallel and equally spaced, showing constant strength
3. Around the positive point charge, the field is radial: electric field strength decreases as distance from the charge increases
4. Field lines are radial, spacing increases with distance, showing decreasing strength

## The Test Charge Requirement

When we define electric field strength, we specify it uses a very small positive test charge. This requirement is commonly tested in explanation questions.

**Test charge** — A positively charged object with very small magnitude of charge, used to measure the electric field at a point.

**Worked example:** Explain why electric field strength is defined in terms of a very small test charge.

1. A large test charge has its own electric field
2. This field will exert a force on the original source charge, causing it to move and alter the original electric field we want to measure
3. A very small test charge has negligible charge, so its own field does not distort the original field, giving an accurate measurement

> **Exam tip:** This explanation is a very common 2-mark question in CIE structured papers, learn the key point about not distorting the original field.

## Common pitfalls

- **Wrong:** Drawing field lines starting at negative charges and ending at positive charges
  - Why it fails: Field lines show the direction of force on a positive test charge, which is attracted to negative charges and repelled by positive charges
  - Correct: Always draw field lines starting on positive charges and ending on negative charges (or infinity for isolated charges)
- **Wrong:** Allowing field lines to cross each other in diagrams
  - Why it fails: If two lines crossed, this would imply two different directions of force at the same point, which is impossible
  - Correct: Draw lines that never cross; mark a null point where the field is zero between two like charges
- **Wrong:** Writing units of $\text{C N}^{-1}$ for electric field strength
  - Why it fails: Electric field strength is force per unit charge $E=F/Q$, so the unit is newtons per coulomb, not coulombs per newton
  - Correct: Remember $E = F/Q$, so units are $\text{N C}^{-1}$ or the equivalent $\text{V m}^{-1}$
- **Wrong:** Assuming electric field is stronger closer to the plates in a uniform field
  - Why it fails: A uniform field by definition has constant strength everywhere between the plates, ignoring edge effects
  - Correct: Recognise equally spaced parallel field lines mean constant uniform electric field strength

## Cheatsheet

| Concept | Key Definition/Formula | Core Property |
| --- | --- | --- |
| Electric field | Region where charge experiences force | Non-contact electrostatic force |
| Electric field strength | $E = F/Q$ | Units: $N C^{-1} = V m^{-1}$ |
| Field lines | Tangent = force on +ve test charge | Start +ve, end -ve, never cross |
| Uniform field | Constant $E$ everywhere | Parallel equally spaced lines, between plates |
| Radial field | $E$ decreases with distance $r$ | Radial lines around point charges |

## What's next

Mastery of electric field concepts is the foundation for all further topics in A2 electrostatics. Next you will learn Coulomb's law, which allows you to calculate the magnitude of electric field strength around point charges, followed by electric potential and potential energy in electric fields. These concepts are then applied to capacitance, energy stored in capacitors, and motion of charged particles in electric fields, all of which are common exam topics worth multiple marks in both paper 1 and paper 2.

- [Electric Potential](https://www.owlsprep.com/study/cie-9702-u21-electric-potential/)
- [Coulomb's Law](https://www.owlsprep.com/study/cie-9702-u21-coulomb-s-law/)
- [Electric field strength](https://www.owlsprep.com/study/cie-9702-u21-electric-field-strength/)

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