Describe an electric field as a region in which an electric charge experiences a force.
1. What is electric charge?
Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electric or magnetic field.
Two types of charge exist: positive and negative.
Like charges repel; unlike charges attract.
Charge is quantised – it occurs in integer multiples of the elementary charge \$e = 1.602 \times 10^{-19}\,\text{C}\$.
Charge is conserved – the total charge in an isolated system remains constant.
2. Units and symbols
Quantity
Symbol
Unit
Electric charge
\$q\$
Coulomb (C)
Elementary charge
\$e\$
Coulomb (C)
3. Electric field – definition
An electric field is a region of space surrounding a charge (or a group of charges) in which another charge would experience an electric force.
4. Representing an electric field
Field lines are used to visualise the direction and relative strength of the field.
Lines start on positive charges and end on negative charges.
The density of lines indicates the magnitude of the field (more lines = stronger field).
The direction of the field at any point is the direction of the force that a positive test charge would feel.
Suggested diagram: Field lines radiating outward from a positive point charge and inward toward a negative point charge.
5. Electric field strength (\$E\$)
The electric field strength \$E\$ at a point is defined as the force \$F\$ experienced by a test charge \$q\$ placed at that point, divided by the magnitude of the test charge:
\$\$
E = \frac{F}{q}
\$\$
Rearranged, the force on a charge in a known field is:
\$\$
F = qE
\$\$
6. Determining the field of a point charge
For a single point charge \$Q\$, the magnitude of the electric field at a distance \$r\$ from the charge is given by Coulomb’s law:
\$\$
E = \frac{1}{4\pi\varepsilon_0}\,\frac{|Q|}{r^{2}}
\$\$
where \$\varepsilon_0 = 8.85 \times 10^{-12}\,\text{C}^2\text{N}^{-1}\text{m}^{-2}\$ is the permittivity of free space.
7. Example problem
Two point charges, \$+5\,\mu\text{C}\$ and \$-3\,\mu\text{C}\$, are placed \$0.20\,\$m apart. Find the magnitude and direction of the electric field at the midpoint.
Calculate the field due to each charge at the midpoint using \$E = \dfrac{1}{4\pi\varepsilon_0}\dfrac{|Q|}{r^{2}}\$ with \$r = 0.10\,\$m.
Because the field direction is away from the positive charge and toward the negative charge, the two fields are in the same direction. Add their magnitudes to obtain the net field.
Result: \$E_{\text{net}} = 2.25 \times 10^{5}\,\text{N\,C}^{-1}\$ directed from the \$+5\,\mu\text{C}\$ charge toward the \$-3\,\mu\text{C}\$ charge.
8. Key points to remember
An electric field exists wherever a charge can experience a force.
The field direction is defined by the force on a positive test charge.
Field strength \$E\$ is measured in newtons per coulomb (N C⁻¹) or volts per metre (V m⁻¹). \$1\;\text{N C}^{-1}=1\;\text{V m}^{-1}\$.
Electric field lines never cross; at any point there is a single, well‑defined direction.
For multiple charges, the net field is the vector sum of the individual fields (superposition principle).
9. Practice questions
State the three fundamental properties of electric charge.
A charge of \$+2\,\mu\text{C}\$ creates an electric field of \$9.0 \times 10^{4}\,\text{N\,C}^{-1}\$ at a certain point. What force would a \$-3\,\mu\text{C}\$ test charge experience at that point? Include direction.
Draw a qualitative field‑line diagram for two equal positive charges separated by a distance \$d\$. Indicate regions where the field strength is greatest.