1.2 Electric Fields

Defining the Electric Field

An electric field is the force per unit charge at a point in space, created by a source charge. Formally, E = F/q. It's a vector field: at every point it has magnitude and direction, pointing away from positive charges and toward negative charges. A test charge placed in the field experiences a force F = qE.

Field from a Point Charge

For a point charge Q, the field at distance r is E = kQ/r², directed radially. This follows directly from Coulomb's law divided by the test charge. Fields from multiple charges obey superposition: add the vector contributions from each source charge to find the net field at a point.

Continuous Charge Distributions

For charge spread over a line, surface, or volume, the field is found by integrating contributions from infinitesimal charge elements dq: dE = k(dq)/r². Symmetry (like uniform rings or rods) often simplifies these integrals by canceling perpendicular components, leaving only the net field along an axis of symmetry.

Key terms

Electric field (definition)

Force per unit charge, E = F/q; a vector pointing away from positive charges and toward negative charges.

Field of a point charge

E = kQ/r², directed radially outward (positive Q) or inward (negative Q).

Superposition principle

The net electric field at a point is the vector sum of the fields due to each individual source charge.

Field from continuous charge distribution

Found by integrating dE = k(dq)/r² over the entire charge distribution.

Test charge

A small hypothetical charge used to measure the electric field without disturbing the source charges.

Try an AP-style question

A −2 μC charge feels a 0.04 N force pointing west. What is the electric field there?

1. 20,000 N/C west
2. 5 × 10⁻⁵ N/C west
3. 0.08 N/C east
4. 20,000 N/C east