Electric potential and equipotential surfaces

Positive test charge in the electric field experiences electric force. Moving against the E-field means that work need be done against the force. The work equals to the increase of electric potential energy of the test charge.









As potential energy describes work done to place the charge in the field, the electric potential describes the field itself. For a radial field of spherical charge (no E-field inside the sphere):

• Equipotential surfaces analogous to height contours in the gravity field. Perpendicular to electric field at any point
• No work need to be done in moving a charge along the surface (no displacement in the direction of E-field)
• Potential decreases in the direction of electric field
• Potential is zero infinitely far away from the source of radial field and at any earthed point.

Consider homogenous E-field between two parallel plates separated by distance d. What is the work done in moving charge Q over the potential difference V? If the bottom of the thundercloud and the Earth surface made up the plate pair separated by 1500 m, what would be the potential difference if the electric field was measured to be 25 kN/C.