Section 4.4: Equipotential Surfaces
Equipotential surfaces are surfaces on which the electric potential is constant. A charge moved along an equipotential surface experiences no work, as the potential energy remains unchanged.
Key Points:
- Work done along an equipotential surface: \( W = 0 \)
- Electric field is always perpendicular to equipotential surfaces.
- Closer surfaces indicate stronger electric fields.
Example 1
Show that no work is done when a charge moves along a spherical equipotential surface around a point charge.
Since the potential \( V = kq/r \) is constant at fixed radius \( r \), \( \Delta U = q \Delta V = 0 \). Thus, \( W = -\Delta U = 0 \).
Example 2
A uniform electric field has parallel equipotential planes separated by 0.5 m. Find the work done by the field on a 2 C charge moving along one plane.
Movement along equipotential: \( W = q \Delta V = 0 \)
Practice Problems
- Explain why the electric field is perpendicular to equipotential surfaces.
- A 1 C charge moves along an equipotential surface. Determine the work done by the field.
- Sketch equipotential surfaces for a dipole.
- Explain the relationship between spacing of equipotential surfaces and electric field strength.
- A charge moves between two points on an equipotential. How does its kinetic energy change?
- Derive the expression for work done in terms of electric potential along a path.
- Show that a conductor in electrostatic equilibrium has equipotential surface throughout.
- Determine the electric field between two parallel equipotential planes 0.2 m apart, potential difference 10 V.
- Explain why no work is done moving a charge along a circular path around a point charge.
- Calculate work done if a charge is moved along a curved equipotential surface near a point charge.