2.4 Forces on Charged Objects

Force from a field

A charged object placed in an electric field experiences a force given by F = qE, where q is the charge and E is the field magnitude. The force is parallel to the field for positive charges and antiparallel for negative charges. This lets you predict acceleration and motion of charged particles in fields.

Superposition of forces

When multiple charges create fields at a point, the total force on a test charge is the vector sum of the individual forces (or equivalently, force = q times the net field). Direction matters — you must add forces as vectors, not just magnitudes, accounting for both magnitude and direction of each contribution.

Uniform fields and motion

In a uniform field (like between parallel plates), a charged particle feels a constant force, producing constant acceleration (a = qE/m). This is analogous to projectile motion under gravity — charges can move in straight lines or parabolic paths depending on initial velocity direction relative to the field.

Key terms

Force on a charge in a field

F = qE; force direction matches field for positive charges, opposite for negative charges.

Superposition principle (forces/fields)

The net force or field from multiple charges is the vector sum of each individual contribution.

Acceleration in a uniform field

a = qE/m; constant force in a uniform field produces constant acceleration.

Motion of charge entering field perpendicular to field lines

Follows a parabolic path, analogous to projectile motion under gravity.

Direction of force on negative charge

Opposite to the direction of the electric field at that point.

Try an AP-style question

The distance between two charges doubles. What happens to the force between them?

1. It becomes ¼ as large
2. It halves
3. It doubles
4. It quadruples