Electric Field Formula

Electric field is a region around a charged object where other charges experience a force.

The Formula

E=Fq=kQr2E = \frac{F}{q} = \frac{kQ}{r^2} where FF is force, qq is test charge, QQ is source charge, rr 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

E⃗\vec{E} is the electric field vector in N/C or V/m, QQ is the source charge in coulombs, rr is the distance in metres, ϵ0≈8.85×10−12\epsilon_0 \approx 8.85 \times 10^{-12} F/m is the permittivity of free space, and k=1/(4πϵ0)≈8.99×109k = 1/(4\pi\epsilon_0) \approx 8.99 \times 10^9 N·m2^2/C2^2.

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 r⃗\vec{r} due to a point charge QQ at the origin is E⃗=14πϵ0Qr2r^\vec{E} = \frac{1}{4\pi\epsilon_0}\frac{Q}{r^2}\hat{r}, where r^\hat{r} is the unit vector pointing from QQ to the field point. For continuous distributions, E⃗=14πϵ0∫dqr2r^\vec{E} = \frac{1}{4\pi\epsilon_0}\int \frac{dq}{r^2}\hat{r}.

Worked Examples

Example 1

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What is the electric field 0.5 m0.5 \text{ m} from a point charge of 4×10−6 C4 \times 10^{-6} \text{ C}? Use k=9×109 N m2/C2k = 9 \times 10^9 \text{ N m}^2/\text{C}^2.

Answer

E=1.44×105 N/CE = 1.44 \times 10^5 \text{ N/C}

First step

1
Electric field from a point charge: E=kqr2E = k\frac{q}{r^2}

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Example 2

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A charge of 2×10−9 C2 \times 10^{-9} \text{ C} is placed in an electric field of 5000 N/C5000 \text{ N/C}. What force does it experience?

Example 3

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A +5 μC+5\ \mu\text{C} point charge sits at the origin. Find the field magnitude at r=0.1 mr = 0.1\ \text{m}. Use k=9×109k = 9\times10^9.

Common Mistakes

  • Confusing electric field with electric force — the field E=F/qE = F/q exists at a point regardless of whether a test charge is present; force requires a charge to act on. - Fix this by naming the system, checking "Am I using a field or potential to explain how one object influences another across space?", and attaching units or direction to the final statement.
  • 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. - Fix this by naming the system, checking "Am I using a field or potential to explain how one object influences another across space?", and attaching units or direction to the final statement.
  • Using the wrong distance — rr is the distance from the source charge to the field point, not between two source charges. - Fix this by naming the system, checking "Am I using a field or potential to explain how one object influences another across space?", and attaching units or direction to the final statement.
  • Using electric field from a keyword alone - Signal words like field, charge, magnet only point to a possible model; the system must match too.

Common Mistakes Guide

If this formula feels simple in isolation but keeps breaking during real problems, review the most common errors before you practice again.

Coulomb's Law Mistakes

Why This Formula Matters

Electric Field gives students a way to explain non-contact forces and energy changes. It connects electricity, magnetism, gravitation, induction, motors, generators, and orbital motion through a shared spatial model.

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?

E⃗\vec{E} is the electric field vector in N/C or V/m, QQ is the source charge in coulombs, rr is the distance in metres, ϵ0≈8.85×10−12\epsilon_0 \approx 8.85 \times 10^{-12} F/m is the permittivity of free space, and k=1/(4πϵ0)≈8.99×109k = 1/(4\pi\epsilon_0) \approx 8.99 \times 10^9 N·m2^2/C2^2.

Why is the Electric Field formula important in Physics?

Electric Field gives students a way to explain non-contact forces and energy changes. It connects electricity, magnetism, gravitation, induction, motors, generators, and orbital motion through a shared spatial model.

What do students get wrong about Electric Field?

Students often know a formula related to electric field but skip the recognition step: Am I using a field or potential to explain how one object influences another across space? That leads to a correct-looking substitution attached to the wrong physical model.

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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