Section 3.4: Equipotential Surfaces
Equipotential surfaces are surfaces on which the electric potential is constant. No work is done when moving a charge along an equipotential surface.
Key Properties:
- Electric field is always perpendicular to equipotential surfaces.
- No work is required to move a charge along an equipotential surface.
- Equipotentials help visualize electric field patterns.
Example 1
Draw equipotential surfaces for a point charge and explain their relation to the electric field.
Equipotential surfaces are concentric spheres centered on the charge. Electric field lines are radial and perpendicular to these spheres.
Practice Problems
- For two equal point charges separated by a distance, sketch the equipotential surfaces.
- Explain why the electric field is zero at the midpoint between two equal and opposite charges.
- For a uniformly charged plane, describe the shape of equipotential surfaces.
- Verify that the work done along an equipotential surface is zero using \( W = -\int \vec{E}\cdot d\vec{l} \).
- Determine the equipotential surfaces for a uniformly charged ring along its axis.