Electric Field Formula

The Formula

E = \frac{F}{q} = \frac{kQ}{r^2} where F is force, q is test charge, Q is source charge, r is distance.

When to use: Every charge creates an invisible 'force zone' around it. Another charge entering this zone feels a push or pull without touching anything.

Quick Example

Hold a charged balloon near small pieces of paper — they jump toward it. The balloon's electric field reaches the paper before any contact.

Notation

\vec{E} is the electric field vector in N/C or V/m, Q is the source charge in coulombs, r is the distance in metres, \epsilon_0 \approx 8.85 \times 10^{-12} F/m is the permittivity of free space, and k = 1/(4\pi\epsilon_0) \approx 8.99 \times 10^9 N·m^2/C^2.

What This Formula Means

A region around a charged object where other charges experience a force. Measured in newtons per coulomb (N/C) or volts per meter (V/m).

Every charge creates an invisible 'force zone' around it. Another charge entering this zone feels a push or pull without touching anything.

Formal View

The electric field at position \vec{r} due to a point charge Q at the origin is \vec{E} = \frac{1}{4\pi\epsilon_0}\frac{Q}{r^2}\hat{r}, where \hat{r} is the unit vector pointing from Q to the field point. For continuous distributions, \vec{E} = \frac{1}{4\pi\epsilon_0}\int \frac{dq}{r^2}\hat{r}.

Worked Examples

Example 1

medium
What is the electric field 0.5 \text{ m} from a point charge of 4 \times 10^{-6} \text{ C}? Use k = 9 \times 10^9 \text{ N m}^2/\text{C}^2.

Solution

  1. 1
    Electric field from a point charge: E = k\frac{q}{r^2}
  2. 2
    E = 9 \times 10^9 \times \frac{4 \times 10^{-6}}{(0.5)^2} = 9 \times 10^9 \times \frac{4 \times 10^{-6}}{0.25}
  3. 3
    E = 9 \times 10^9 \times 1.6 \times 10^{-5} = 1.44 \times 10^5 \text{ N/C}

Answer

E = 1.44 \times 10^5 \text{ N/C}
The electric field describes the force per unit charge at a point in space. It points radially outward from positive charges and inward toward negative charges.

Example 2

medium
A charge of 2 \times 10^{-9} \text{ C} is placed in an electric field of 5000 \text{ N/C}. What force does it experience?

Common Mistakes

  • Confusing electric field with electric force — the field E = F/q exists at a point regardless of whether a test charge is present; force requires a charge to act on.
  • Forgetting that electric field is a vector: when multiple charges are present, you must add their fields using vector addition, not just add the magnitudes.
  • Using the wrong distance — r is the distance from the source charge to the field point, not between two source charges.

Why This Formula Matters

Electric fields explain how charges influence each other without contact and are the basis of capacitors, antennas, and electromagnetic waves.

Frequently Asked Questions

What is the Electric Field formula?

A region around a charged object where other charges experience a force. Measured in newtons per coulomb (N/C) or volts per meter (V/m).

How do you use the Electric Field formula?

Every charge creates an invisible 'force zone' around it. Another charge entering this zone feels a push or pull without touching anything.

What do the symbols mean in the Electric Field formula?

\vec{E} is the electric field vector in N/C or V/m, Q is the source charge in coulombs, r is the distance in metres, \epsilon_0 \approx 8.85 \times 10^{-12} F/m is the permittivity of free space, and k = 1/(4\pi\epsilon_0) \approx 8.99 \times 10^9 N·m^2/C^2.

Why is the Electric Field formula important in Physics?

Electric fields explain how charges influence each other without contact and are the basis of capacitors, antennas, and electromagnetic waves.

What do students get wrong about Electric Field?

Field lines point in the direction a positive test charge would move — away from positive, toward negative.

What should I learn before the Electric Field formula?

Before studying the Electric Field formula, you should understand: electric charge, force.

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