Electric Potential

Electric Potential The change in potential energy is the negative of the work done by the field. E A B 1V = 1J/C 1eV=1.6× J

Voltage from a Sphere Ex. What is the electric potential (voltage) between the surface of a sphere with radius 1m and a point 0.5 m from the surface if the sphere has a charge of +4  C? B A

Different Fields Uniform field Point Charge If starting location (reference) is a infinity, then

Superposition Using infinity as a reference point, we can find the net voltage from multiple charges. Notice that we are adding scalars, not vectors.

For the diagram to the right what is the voltage at the origin where 0 volts is at infinity?  3 mC +6 mC

E Field from Electric Potential The rate at which voltage changes is related to the strength of the electric field. Considering all three dimensions we get

Find the E Field What is the electric field at (3m, 2m) for the following voltage function? Taking the appropriate derivatives gives an electric field of Evaluating that field at (3m, 2m) gives

FYI Using Maple we can visualize the electric field and equipotential lines.

Equipotential Surfaces Surfaces which are at the same voltage level. Equipotential surfaces intersect electric field lines perpendicularly. The surface of a charged conducting object is at the same electric potential. Any point within a conductor is at the same potential as its surface.

Continuous Charge If charge is distributed over an object, then Ex. An electron is placed 5 m on axis from a uniformly charged ring. The ring is 0.03 m in radius and has a charge per length of 3  C/m. What is the speed of the electron as it passes through the loop?

Lightning Air ionizes with an electric field of 75,000 volts per inch. Lightning takes the easiest path from its perspective. Rapidly expanding air forms a shock wave called thunder.