Describe an electric field as a region in which an electric charge experiences a force

4.2.1 Electric Charge: Electric Fields

What is an Electric Field?

⚡️ An electric field is a region of space where an electric charge experiences a force. Think of it as an invisible wind that pushes on a tiny ball. If you place a small charged particle in this region, the particle feels a pull or push depending on its charge.

The field is described by the vector quantity \$E\$ (electric field strength). The force on a charge \$q\$ is given by the simple relation:

\$F = qE\$

Key point: If \$q>0\$, the force points in the same direction as the field; if \$q<0\$, it points opposite.

Calculating the Field from a Point Charge

For a single point charge \$Q\$, the electric field at a distance \$r\$ is:

\$E = \frac{1}{4\pi\epsilon_0}\frac{Q}{r^2}\$

Example: Let \$Q = +2\,\mu\text{C}\$ and \$r = 0.1\,\text{m}\$. Using \$\frac{1}{4\pi\epsilon_0} \approx 9.0\times10^9\,\text{N·m}^2/\text{C}^2\$,

  1. Convert \$Q\$: \$2\,\mu\text{C} = 2\times10^{-6}\,\text{C}\$.
  2. Compute \$E\$: \$E = 9.0\times10^9 \times \frac{2\times10^{-6}}{(0.1)^2} = 1.8\times10^6\,\text{N/C}\$.

The field points radially outward from a positive charge and inward toward a negative charge.

Exam Tip

• Always remember that the electric field is defined as the force per unit charge: \$E = \frac{F}{q}\$.

• Check units: the field is measured in newtons per coulomb (N/C).

• When given a force and a charge, you can find the field directly: \$E = F/q\$.

• For point charges, use the inverse square law formula above.

• Pay attention to the sign of the charge – it determines the direction of the field relative to the charge.

Key Points Summary

  • The electric field is a vector field that exerts a force on charges.
  • Force on a charge: \$F = qE\$.
  • Field from a point charge: \$E = \frac{1}{4\pi\epsilon_0}\frac{Q}{r^2}\$.
  • Field direction depends on the sign of the test charge.
  • Units of \$E\$ are N/C.

Quick Review Quiz

1️⃣ If a charge of \$-3\,\text{C}\$ is placed in a field of \$5\,\text{N/C}\$, what is the magnitude and direction of the force?


2️⃣ A point charge of \$+4\,\text{nC}\$ is 0.2 m from a test charge. What is the electric field at that point?


Use the formulas above to solve.