What are electric fields? Revision Notes for AQA A-Level Physics

What are electric fields?

Introduction

Charged objects produce an electric field in the region surrounding them. Any charged particle or object placed within this region experiences a force due to the electric field.

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An electric field is a region of space where charged particles experience a force. The field exists whether or not another charge is present to experience it.

Field line representation

Electric fields are represented using field lines with arrows indicating the field direction. To determine the direction at any point in the field, imagine placing a small positive test charge at that location. The direction of the force acting on this test charge indicates the direction of the field line at that point.

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The test charge is always assumed to be positive by convention. This standardization allows us to consistently represent field directions across all electric field scenarios.

Field patterns around charged spheres

For an isolated metal sphere with positive charge, the electric field is a radial field with field lines pointing outward from the sphere. If the sphere had negative charge, the field lines would point radially inward toward the sphere.

When two metal spheres are placed near each other:

If one sphere is negative and the other positive, the field lines form curved paths connecting the two spheres, pointing from positive to negative
If both spheres have positive charge, the field pattern shows field lines repelling each other between the spheres

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The spacing of field lines indicates field strength: closer field lines represent a stronger electric field.

Electric field strength

The electric field strength at a point is defined using the force experienced by a small positive test charge placed at that location.

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The test charge must be sufficiently small in both size and charge to avoid distorting the electric field being measured. If the test charge is too large, it will alter the field you're trying to measure!

Coulomb's law

Coulomb's law gives the electrostatic force between two point charges in a vacuum:

$F = \frac{Q_1Q_2}{4\pi\varepsilon_0r^2}$

where:

F is the electrostatic force (N)
Q₁ and Q₂ are the two point charges (C)
r is the separation between the charges (m)
ε₀ is the permittivity of free space (F m⁻¹)

This equation also applies to charges in air, which behaves similarly to a vacuum for electric field calculations.

The permittivity of free space (ε₀) has a value of 8.85 × 10⁻¹² F m⁻¹.

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Worked Example: Calculating Electrostatic Force

Two point charges, Q₁ = +2.0 × 10⁻⁶ C and Q₂ = +3.0 × 10⁻⁶ C, are separated by a distance of 0.50 m in a vacuum. Calculate the electrostatic force between them.

Step 1: Identify the known values

Q₁ = +2.0 × 10⁻⁶ C
Q₂ = +3.0 × 10⁻⁶ C
r = 0.50 m
ε₀ = 8.85 × 10⁻¹² F m⁻¹

Step 2: Apply Coulomb's law

$F = \frac{Q_1Q_2}{4\pi\varepsilon_0r^2}$

Step 3: Substitute the values

$F = \frac{(2.0 \times 10^{-6})(3.0 \times 10^{-6})}{4\pi(8.85 \times 10^{-12})(0.50)^2}$

Step 4: Calculate

$F = \frac{6.0 \times 10^{-12}}{4\pi(8.85 \times 10^{-12})(0.25)} = 0.216 \text{ N}$

The electrostatic force between the charges is 0.22 N (to 2 s.f.)

Since both charges are positive, this is a repulsive force.

Key principles

A uniformly charged sphere can be treated as a point charge located at the centre of the sphere when calculating electric fields and forces at external points.

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Electrostatic forces between subatomic particles are many orders of magnitude greater than gravitational forces between the same particles. This explains why electric forces dominate at the atomic scale despite gravity being the dominant force on larger scales.

For example, the electrostatic force between a proton and electron in a hydrogen atom is approximately 10³⁹ times stronger than the gravitational force between them!

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Key Points to Remember:

Electric fields exist around all charged objects and exert forces on other charges placed within them
Field lines point away from positive charges and toward negative charges; closer lines indicate stronger fields
Electric field strength is defined using the force on a small positive test charge
Coulomb's law: $F = \frac{Q_1Q_2}{4\pi\varepsilon_0r^2}$ describes the force between point charges
Electrostatic forces between subatomic particles are far stronger than gravitational forces at that scale

What are electric fields? (AQA A-Level Physics): Revision Notes