What is \(\Delta V\) between two points on the same equipotential surface?

How much work does the electric force do when a charge moves along an equipotential surface?

Are electric field lines parallel or perpendicular to equipotential surfaces?

A \(+5.0\,\mathrm{nC}\) charge moves along an equipotential from one point to another. Find \(\Delta U\).

In a uniform electric field pointing in the \(+x\) direction, what is the orientation of equipotential lines in an \(x\)-\(y\) sketch?

If neighboring equipotential surfaces are very close together in one region, what does that suggest about the electric field magnitude there?

Explain why the surface of a conductor in electrostatic equilibrium is an equipotential.

A charge moves from \(V=120\,\mathrm{V}\) to another point on the same conductor surface in electrostatic equilibrium. What are \(\Delta V\), \(\Delta U\), and \(W_{\mathrm{elec}}\)?

A proposed diagram shows equipotential lines crossing electric field lines at non-right angles and also shows field lines lying along one equipotential. Identify the errors using work and tangent-component reasoning.

A uniform electric field has magnitude \(E\). A family of parallel equipotential planes is separated by distance \(d\) measured along the field direction. Derive the potential difference between adjacent planes and explain how the sign depends on moving with or against \(\vec E\).