AeroLab Reading room

Physics / A2 level

Electric fields

Distinguish the direction of force from scalar electric potential.

Learning objectives

The big idea

Electric field strength is force per unit positive test charge. A negative charge experiences a force opposite to the field direction. Field lines describe a vector field; they are not paths that every moving charge must follow.

Potential is energy per unit charge. Point-charge field strength falls as inverse distance squared, while potential varies as inverse distance. Between closely spaced parallel plates away from edges, a uniform-field approximation can be useful.

1. A field is defined using a positive test charge

Electric field strength is force per unit positive test charge. A positive charge accelerates along the field if no other force acts, while a negative charge feels force in the opposite direction. Field lines represent the field, not guaranteed particle paths: a charge may already have transverse velocity. Around a point charge, field strength magnitude varies as 1/r².

2. Potential is an energy quantity

Electric potential is potential energy per unit charge, usually measured relative to a stated zero. For an isolated point charge with zero at infinity, V = Q/(4πε₀r). Potential contributions add as scalars; field contributions add as vectors. At the midpoint of equal positive and negative charges, potentials cancel while their fields reinforce. Zero potential therefore does not imply zero field.

3. Uniform fields make useful approximations

Between closely spaced parallel plates, away from edges, E ≈ ΔV/d. This is not the general expression for every electric field. A 200 V difference across 0.010 m corresponds to about 20000 V/m. Edge regions curve the field, so a real deflection experiment must consider the region traversed. The field direction points towards decreasing potential, opposite the potential gradient.

4. Connect forces to energy changes

A charge moved through a potential difference changes electric potential energy by qΔV. A freely accelerated charge can convert that change into kinetic energy when other transfers are negligible. Track the sign of q and the initial and final potentials; an electron need not move towards lower potential energy by moving towards lower electric potential. Potential and potential energy are related but not interchangeable.

A method you can reuse

  1. Draw source charges, field directions and chosen positions.
  2. Choose point-charge or uniform-field equations appropriately.
  3. Add field vectors and potential scalars separately.
  4. Use the charge sign in force and energy calculations.
  5. Check reference potential, distance and any edge-effect approximation.
Why can an electron accelerate towards a higher electric potential?

Its charge is negative, so increasing electric potential decreases its electric potential energy. That decrease can supply kinetic energy as the electric force accelerates it.

Equations and relationships

F=qEF=qE

The sign of q determines the force direction.

E=VdE=\frac Vd

Uniform-field magnitude between plates separated by d.

V=Q4πε0rV=\frac{Q}{4\pi\varepsilon_0r}

Potential of an isolated point charge with zero at infinity.

Worked example

A +2.0 μC charge is in a field of 3000 N/C. What force magnitude acts?

Follow the solution

F = qE = 2.0 × 10⁻⁶ × 3000 = 0.006 N.

Investigate and explain

Place equal positive and negative simulated charges symmetrically. Investigate potential and field at their midpoint.

Compare field arrows with potential contours, then inspect a parallel-plate field. A static charging demonstration does not replace quantitative field calculations or represent every particle trajectory.

Open the interactive investigation

Check your understanding

1. In which direction is the force on a negative test charge?

  1. Always along the electric field
  2. Opposite to the electric field
  3. Always perpendicular to the electric field
Check the answer and reasoning

Opposite to the electric field

F = qE reverses direction when q is negative.

2. A +2.0 μC charge is in a field of 3000 N/C. What force magnitude acts?

  1. 6000 N
  2. 0.0015 N
  3. 0.006 N
Check the answer and reasoning

0.006 N

F = qE = 2.0 × 10⁻⁶ × 3000 = 0.006 N.

3. What is electric potential?

  1. Potential energy per unit charge
  2. Force per unit mass
  3. Charge flowing per second
Check the answer and reasoning

Potential energy per unit charge

Potential has units J/C, equivalent to volts.