# Electric fields

> IB Physics SL · Unit 4: Fields
> Source: https://www.owlsprep.com/study/ib-physics-sl-u4-electric-fields/

This sub-topic introduces the concept of electric fields, how to represent them diagrammatically, and how to calculate electric field strength for both uniform and radial fields, a core foundation for electrostatics in IB Physics SL.

**Prerequisites:** [Coulomb's law for electrostatic force](https://www.owlsprep.com/study/ib-physics-sl-u4-coulombs-law/); [Fundamentals of electric charge](https://www.owlsprep.com/study/ib-phys-sl-u3-electric-charge/)

## Learning objectives

- Define electric field and electric field strength
- Calculate electric field strength for radial and uniform electric fields
- Correctly draw and interpret electric field line diagrams
- Compare properties of radial and uniform electric fields

## What is an electric field?

**Electric field** — A field is a region of space where a force acts on an object with a specific property. For electric fields, that property is electric charge: an electric field is a region of space around any charged object where another charged object experiences an electrostatic force.

*Example:* A proton has an electric field around it that attracts electrons and repels other protons.

The field model solves the problem of "action at a distance": rather than charges interacting directly across empty space, a charge modifies the space around it, and any other charge in that space interacts directly with the field.

**Check your understanding**

Test your basic understanding

1. Which of the following best describes an electric field?

   - A type of energy stored around charges
   - A region of space where charged objects experience force
   - The force between two charged objects
   - The total charge in a region of space

   *Answer:* A region of space where charged objects experience force

   *Why:* Correct! The field is the region where force acts, not the force itself.

**Worked example:** A small test charge of +1.0 × 10⁻⁹ C experiences an electrostatic force of 2.0 × 10⁻⁵ N at a point in an electric field. Calculate the electric field strength at this point.

1. Use the general definition of electric field strength:
2. $$E = \frac{F}{q}$$
3. Substitute the given values:
4. $$E = \frac{2.0 \times 10^{-5}}{1.0 \times 10^{-9}} = 2.0 \times 10^4 \text{ N C}^{-1}$$

## Electric field strength for point charges

**Electric field strength** — Force per unit positive test charge at a point in an electric field. The test charge must be small enough that it does not disturb the field it measures.

*Notation:* $E$

$$E = \frac{F}{q}$$

We can derive the formula for electric field strength around a point charge using Coulomb's law. Force between source charge $Q$ and test charge $q$ is $F = \frac{kQq}{r^2}$. Substituting into $E = \frac{F}{q}$ cancels out $q$, giving the formula below.

$$E = \frac{kQ}{r^2}$$

**Worked example:** Calculate the electric field strength at a point 0.5 m away from a stationary point charge of +2.0 × 10⁻⁶ C. Use $k = 9.0 × 10^9 \text{ N m}^2 \text{ C}^{-2}$.

1. Recall the formula for electric field strength around a point charge:
2. $$E = \frac{kQ}{r^2}$$
3. Substitute the given values:
4. $$E = \frac{(9.0 \times 10^9)(2.0 \times 10^{-6})}{(0.5)^2}$$
5. Calculate the magnitude and state direction:
6. $$E = 7.2 \times 10^4 \text{ N C}^{-1}, \text{ directed radially outward}$$

> **Exam tip:** Always state the direction of the electric field, as it is a vector quantity. Examiners regularly award a separate mark for direction.

## Representing electric fields with field lines

Electric fields are invisible, so we use electric field lines (lines of force) to represent their direction and relative strength. There are standard rules for drawing valid field line diagrams:

- Field lines start on positive charges and end on negative charges (or infinity for isolated charges).
- The direction of the field line at any point is the direction of force a positive test charge would experience.
- Closer spacing of field lines means a stronger electric field.
- Field lines never cross each other, as the field can only have one direction at any point.

**Worked example:** Describe the electric field lines for (a) an isolated positive point charge, (b) two parallel oppositely charged plates.

1. For an isolated positive point charge: Field lines radiate outward equally in all directions. Spacing increases with distance from the charge to show decreasing field strength.
2. For two parallel oppositely charged plates: Field lines are straight, parallel, and equally spaced between the plates (showing a uniform field), curving only at the edges (edge effect). Lines run from the positive plate to the negative plate.

## Uniform vs radial electric fields

**Comparing methods**

The two most common electric fields tested at IB SL are uniform and radial, with distinct properties:

- **Radial field (point charge)** — Field around a single point charge. Field strength decreases with the square of distance from the charge. Direction is radial.
  - Pros: Simple derivation from Coulomb's law
  - Cons: Strength varies with position

- **Uniform field (parallel plates)** — Field between two parallel oppositely charged plates connected to a potential difference $V$. Field strength is constant everywhere between the plates. Direction is perpendicular to plates from positive to negative.
  - Pros: Constant strength simplifies calculations
  - Cons: Only uniform away from plate edges

| Property | Radial field | Uniform field |
| --- | --- | --- |
| Field strength equation | $E = \frac{kQ}{r^2}$ | $E = \frac{V}{d}$ |
| Variation of strength | Decreases with $r^2$ | Constant everywhere |
| Field line spacing | Increases with distance | Equal everywhere |
| Direction | Radial (out/in) | Uniform perpendicular |

**Worked example:** Two parallel plates are separated by 0.02 m and have a potential difference of 100 V between them. What is the electric field strength between the plates?

1. Use the uniform field formula:
2. $$E = \frac{V}{d}$$
3. Substitute values:
4. $$E = \frac{100}{0.02} = 5000 \text{ V m}^{-1} = 5.0 \times 10^3 \text{ N C}^{-1}$$

## Common pitfalls

- **Wrong:** Forgetting to state the direction of the electric field.
  - Why it fails: Electric field strength is a vector, and examiners often award a separate mark for direction that many students miss.
  - Correct: Always add direction: outward from positive charges, inward to negative charges, from positive to negative plate for uniform fields.
- **Wrong:** Confusing the general definition formula with specific field formulas.
  - Why it fails: Students often try to use $E = \frac{kQ}{r^2}$ for uniform field problems, leading to incorrect results.
  - Correct: Remember: $E = \frac{F}{q}$ (general definition), $E = \frac{kQ}{r^2}$ (point charge), $E = \frac{V}{d}$ (uniform parallel plates).
- **Wrong:** Drawing crossing electric field lines.
  - Why it fails: Students incorrectly assume two fields can give two different directions at the same point.
  - Correct: Field lines never cross, because the resultant field at any point has only one direction.
- **Wrong:** Claims field strength is stronger near the plates in a parallel plate uniform field.
  - Why it fails: Students transfer radial field behavior (stronger closer to the charge) to uniform fields incorrectly.
  - Correct: Between parallel oppositely charged plates, field strength is constant everywhere away from the edges.

## Cheatsheet

| Field type | Formula | Key properties |
| --- | --- | --- |
| General definition | $E = \frac{F}{q}$ | Force per unit positive test charge, units $\text{N C}^{-1} = \text{V m}^{-1}$ |
| Radial (point charge) | $E = \frac{kQ}{r^2}$ | Vector, direction radial, $E \propto 1/r^2$ |
| Uniform (parallel plates) | $E = \frac{V}{d}$ | Vector, direction $+ \to -$, constant strength |
| Field line rules |  | Start on +, end on -, never cross, closer lines = stronger field |

## What's next

Electric fields are a core foundation for understanding electric potential, capacitance, and electromagnetic induction, all key assessed topics in IB Physics SL. The field model introduced here is also generalizable to gravitational fields, which share many identical mathematical structures, so mastering electric fields makes learning gravitational concepts much simpler. Examiners regularly test understanding of electric field properties and calculations in both Paper 1 and Paper 2, so solidifying this knowledge will pay off across multiple exam questions. Next, you can explore electric potential and potential difference, which describe energy storage and work in electric fields.

- [Gravitational fields](https://www.owlsprep.com/study/ib-physics-sl-u4-gravitational-fields/)
- [Magnetic fields](https://www.owlsprep.com/study/ib-physics-sl-u4-magnetic-fields/)

---

From [OwlsPrep](https://www.owlsprep.com) — free study guides for A-Level, IB, AP and IGCSE, written against the official syllabus. Canonical page: https://www.owlsprep.com/study/ib-physics-sl-u4-electric-fields/