Electric Potential Physics Department, New York City College of Technology

Key words Electric potential energy Electric potential Electric field Equipotential lines Principle of superposition

Electric potential energy The electrostatic force is a conservative force We can thus define electric potential energy PE:, which means that when a point charge q moves from point a to point b, the change in electric potential energy, is the negative of the work done by the electric force to move the charge from a to b. Since, we have

Electric potential and potential difference Electric potential If a positive test charge q has electric potential energy PE a at point a, the electric potential V a at this point is The unit is Volt (V). V doesn’t depend on q. The difference in electric potential between point a and point b is

Electric potential and electric field Since and we have, or

Example #1 Calculate the magnitude of the electric field.

Equipotential lines Equipotential lines or surfaces An equipotential surface is one on which all points are at the same potential. An equipotential surface must be perpendicular to the electric field at any point.

Equipotential lines—continued Solid red: electric field lines Dashed green: equipotential lines

Electric potential due to point charges Potential due to a point charge Q ( with V ∞ =0) Potential due to a collection of point charges is all the potentials added as scalars:

Example #2 Determine the potential at a point 0.50m (a) from a +20  C point charge, (b) from a -20  C point charge. (a) (b)

Example #3 Calculate the electric potential (a) at point A, and (b) at point B.

Example #3--continued