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

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.