Field of a Point Charge
Electric field around a point charge.
Formula
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How it works
A point charge creates an electric field that spreads out radially in all directions, getting weaker as you move farther away. The formula E = kq/r^2 comes from Coulomb’s law: the force on a tiny positive test charge is proportional to the source charge and inversely proportional to the square of the distance, and electric field is defined as force per unit test charge. The sign of q tells you the direction of the field: away from a positive charge and toward a negative charge.
When to use it
Use this formula when you need the electric field produced by a single isolated charge, or when a problem treats a charged object as a point charge because its size is negligible compared with the distance. It is especially useful in electrostatics problems involving forces on other charges, field strength at a location, or comparing how field changes with distance.
Worked example, step by step
Find the electric field 0.20 m from a point charge of +3.0 × 10^-6 C. E = kq/r^2 E = (8.99 × 10^9)(3.0 × 10^-6)/(0.20)^2 E = (2.697 × 10^4)/0.040 E = 6.7425 × 10^5 N/C Rounded to 2 significant figures: E ≈ 6.7 × 10^5 N/C Direction: radially outward, because the charge is positive.
Common mistakes to avoid
- Forgetting to square the distance r in the denominator
- Using the wrong direction for the field when the charge is negative
- Mixing up electric field with electric force and forgetting that E is force per unit charge
Did You Know?
A point charge's field weakens with the square of distance, the same inverse-square pattern as gravity.
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