Lesson 4 of 13 · 7 min
Equipotential surfaces
NCERT §2.6
Meera wants a map of the dome's potential, the way a hill map shows height with contour lines. What shape are the lines of equal potential, and what do they say about the field?
The lesson in notes
In short
An equipotential surface is one on which V has the same value at every point. Moving a charge along it needs no work.
The field is everywhere at right angles to the equipotential surface through that point; if it had a component along the surface, moving along it would take work.
Shapes: concentric spheres around a point charge; planes at right angles to the field in a uniform field; distorted closed surfaces around a dipole or two like charges.
Field and potential: E = −δV/δl, so the size of E is the drop in potential per unit distance taken at right angles to the equipotentials.
E points in the direction in which V decreases fastest (the steepest fall of potential).
Where equipotentials drawn at equal steps of V crowd together the field is strong; where they spread apart it is weak.
In a uniform field E, two planes a distance d apart along the field differ in potential by Ed.