2.7 Isolines and Electric Fields

Equipotential lines (isolines)

Equipotential lines connect points of equal electric potential around a charge or charge configuration. No work is done moving a charge along an equipotential line, since potential doesn't change. Around a point charge, equipotential lines are concentric circles (spheres in 3D); between parallel plates, they are straight lines parallel to the plates.

Fields are perpendicular to equipotentials

Electric field lines always cross equipotential lines at right angles, pointing from high to low potential. Field lines show the direction of force on a positive charge; equipotentials show where potential energy stays constant. Where equipotential lines are closely spaced, the field is strong; widely spaced lines mean a weak field.

Reading field strength from spacing

The magnitude of the electric field relates to how quickly potential changes with distance: E = −ΔV/Δd. Closely packed equipotential lines indicate a rapidly changing potential, meaning a strong field. This lets you estimate relative field strength directly from a diagram of isolines without doing detailed calculations.

Key terms

Equipotential line

A line (or surface) connecting points of equal electric potential; no work is done moving a charge along it.

Relationship between field lines and equipotentials

Electric field lines are always perpendicular to equipotential lines and point from high to low potential.

Equipotentials around a point charge

Concentric circles (spheres in 3D) centered on the charge.

Equipotentials between parallel plates

Straight lines parallel to the plates, evenly spaced in a uniform field.

Field strength from isoline spacing

Closely spaced equipotential lines = strong field; widely spaced lines = weak field (E = −ΔV/Δd).

Try an AP-style question

How are equipotential lines oriented relative to electric field lines?

1. At 45°
2. Perpendicular
3. Parallel
4. They never meet