understand that an electric field is an example of a field of force and define electric field as force per unit positive charge

Published by Patrick Mutisya · 14 days ago

Electric Fields and Field Lines – A-Level Physics 9702

Electric Fields and Field Lines

Learning Objective

Understand that an electric field is an example of a field of force and define the electric field as the force per unit positive charge.

What is a Field?

A field is a region of space in which a force can be experienced by a test object placed within it. In mechanics we encounter gravitational fields; in electromagnetism we encounter electric and magnetic fields.

Definition of Electric Field

The electric field \$\mathbf{E}\$ at a point is defined as the force \$\mathbf{F}\$ experienced by a small positive test charge \$q_{0}\$ placed at that point, divided by the magnitude of the test charge:

\$\mathbf{E} = \frac{\mathbf{F}}{q_{0}}\$

Because the test charge is taken to be positive, the direction of \$\mathbf{E}\$ is the direction of the force on a positive charge.

Properties of Electric Fields

PropertyExplanation
Vector quantityHas both magnitude and direction; represented by arrows.
UnitsNewtons per coulomb (N C⁻¹) or volts per metre (V m⁻¹).
SuperpositionThe net field is the vector sum of fields due to individual charges.
SourceArises from electric charges and changing magnetic fields (Maxwell’s equations).

Electric Field Lines

Field lines are a visual tool to represent the direction and relative strength of an electric field.

  • Lines originate on positive charges and terminate on negative charges.

  • The tangent to a field line at any point gives the direction of \$\mathbf{E}\$ there.

  • The density of lines (lines per unit area) is proportional to the magnitude of the field.

  • Field lines never cross; crossing would imply two different directions for \$\mathbf{E}\$ at the same point.

Constructing Field Lines for Simple Charge Configurations

  1. Single positive charge \$+Q\$: Radial lines emanate outward uniformly.

  2. Single negative charge \$-Q\$: Radial lines converge inward uniformly.

  3. Equal opposite charges (dipole): Lines emerge from \$+Q\$, curve, and end on \$-Q\$, with a denser region between the charges.

  4. Like charges \$+Q\$ and \$+Q\$: Lines emerge from each charge and repel each other, creating a region of low line density between them.

Suggested diagram: Field lines for a positive point charge, a negative point charge, and an electric dipole.

Using the Definition in Calculations

Given a point charge \$Q\$, the magnitude of the electric field at a distance \$r\$ from the charge is derived from Coulomb’s law:

\$E = \frac{1}{4\pi\varepsilon_{0}}\,\frac{|Q|}{r^{2}}\$

Direction is radially outward for \$Q>0\$ and radially inward for \$Q<0\$.

Key Points to Remember

  • The electric field is a vector field that exists whether or not a test charge is present.

  • It is defined as force per unit positive test charge: \$\mathbf{E} = \mathbf{F}/q_{0}\$.

  • Field lines provide a qualitative picture: direction (tangent) and strength (density).

  • Superposition allows us to add fields from multiple sources vectorially.

Practice Questions

  1. Two point charges, \$+5\,\mu\text{C}\$ and \$-5\,\mu\text{C}\$, are 0.10 m apart. Sketch the field lines and indicate the direction of the field at the midpoint.

  2. A test charge \$q_{0}=2\,\text{nC}\$ experiences a force of \$3\times10^{-6}\,\text{N}\$ to the right. Calculate the electric field at that point.

  3. Explain why field lines never intersect, using the definition of the electric field.