The Electric Field

You’ll be able to

Define the electric field as force per unit charge and state its units
Calculate the field produced by a point charge and the force it exerts on a test charge
Interpret electric field lines and the direction of the field around charges

Force at a distance, reimagined

Rather than say two charges reach across empty space to push each other, physics says each charge fills the space around it with an electric field — a condition that any other charge then feels. The field E at a point is the force per unit positive charge that would act there: strong where the force on a test charge would be strong. This lets us describe the influence of a charge arrangement before we ever place a second charge in it.

Electric field: definition and point-charge value

E = F / q and E = k · |Q| / r²

Units are N·C⁻¹ (equivalently V·m⁻¹). The first form gives the force felt by a charge q in a field; the second gives the field a source charge Q creates at distance r.

Direction and field lines

The electric field is a vector: it has direction as well as magnitude. By convention it points the way a positive test charge would be pushed — away from positive source charges and toward negative ones. We picture fields with field lines: they start on positive charges and end on negative ones, never cross, and crowd together where the field is strong. The force on a charge placed in the field is F = qE; a negative charge feels a force opposite to the field direction.

Worked example

A +5.0 µC point charge sits alone. What is the electric field it produces at a point 0.10 m away, and which way does it point?

1.Use the point-charge field: E = k|Q| / r².
2.Substitute: E = (9.0 × 10⁹)(5.0 × 10⁻⁶) / (0.10)².
3.Numerator: 9.0 × 10⁹ × 5.0 × 10⁻⁶ = 4.5 × 10⁴.
4.Divide by r² = 0.010: 4.5 × 10⁴ / 0.010 = 4.5 × 10⁶ N·C⁻¹.

Answer: ≈ 4.5 × 10⁶ N·C⁻¹, pointing radially away from the positive charge.

Checkpoint

A charge of +2.0 µC placed at a point experiences a force of 0.10 N. What is the magnitude of the electric field at that point?

Tip

To find the field, imagine removing whatever charge is sitting at the point and asking “what would a lone +1 C feel here?” The field belongs to the source charges; it exists whether or not a test charge is present.

Checkpoint

What is the magnitude of the electric field produced by a +4.0 µC point charge at a distance of 2.0 m?

On the exam

Two different formulas share the letter E. Use E = F/q when a charge and the force on it are given; use E = kQ/r² when a source charge and a distance are given. Mixing them up is a classic slip.

Answer the 2 checkpoints as you read.