Electric Field
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 5 practice questions.
A charge creates an electric field around it: the force per coulomb that any other charge would feel there, E = F/q. It points away from positive charges and toward negative ones, and fields from several charges add as vectors.
1. Field from point charges
2. Reading field lines
Field lines start on positive charges and end on negative ones. The field at a point is tangent to the line there.
Closer lines mean a stronger field. Lines never cross.
Between two oppositely charged parallel plates, the field is uniform: same size and direction everywhere. A charge there feels a constant force, so it moves like a projectile.
The field doesn’t depend on the test charge you use to measure it. Double the test charge and the force doubles, but F/q stays the same.
3. Example, then try it
Find the electric field 0.30 m from a +4.0 nC charge. What force would an electron feel there?
E = (9.0 × 10⁹)(4.0 × 10⁻⁹) ÷ (0.30)² = 36 ÷ 0.090 = 400 N/C, pointing away from the charge.
F = qE = (1.6 × 10⁻¹⁹)(400) = 6.4 × 10⁻¹⁷ N, toward the charge (an electron is negative).
A +4.0 nC charge sits at x = 0 and a −4.0 nC charge at x = 0.60 m. Find the electric field at the midpoint. What force would a proton feel there?
From +4.0 nC: r = 0.30 m, so E = 400 N/C, pointing away from it: +x.
From −4.0 nC: also 400 N/C, pointing toward it: also +x.
Net field: same direction, so they add: 800 N/C in the +x direction.
Proton: F = (1.6 × 10⁻¹⁹)(800) ≈ 1.3 × 10⁻¹⁶ N, in the +x direction.
Answer: 800 N/C toward the negative charge; 1.3 × 10⁻¹⁶ N on a proton.
4. Common mistakes
The test charge used to measure the electric field at a point is doubled. What happens to the field at that point?
The force on the test charge doubles, but E = F/q stays the same. The field comes from the source charges.
Ready to practice?
5 questions on Electric Field, each with a hint and an explanation for every wrong answer.