Physics 014 Electric Potential Topics o o Electric

Topics o o Electric Potential Energy Electric Potential Equipotential surfaces Calculating Potential from the

Electric Potential Energy o Consider the following paths in an electric field

Electric Potential Energy o We can assign an electric potential energy (U) to a

Electric Potential Energy o If Ui =0, then the final potential energy of the

Electric Potential Energy o Example: Near Earth’s surface the electric field has the magnitude

Electric Potential Energy Given: Calculation: Eqn:

? ? ? In the figure, a proton moves from point i to point

Electric Potential o o It is useful to define the electric potential (or potential)

Electric Potential o The electric potential difference between two points i and f is

Electric Potential o Suppose we must apply a force to move a particle in

? ? ? We move a proton from point i to point f in

Equipotential Surfaces o Adjacent points that have the same electric potential form an equipotential

Potentials and Fields o If I only have the electric field how do I

Potentials and Fields o We take the line integral (a particular path) between two

? ? ? o For a family of equipotential surfaces and five paths of

Electric Potential Energy o Sometimes (not always) we will take the reference position (U=0)

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Physics 014 Electric Potential

Topics o o Electric Potential Energy Electric Potential Equipotential surfaces Calculating Potential from the field

Electric Potential Energy o Consider the following paths in an electric field

Electric Potential Energy o We can assign an electric potential energy (U) to a system of two or more particles Work done by force Final state Initial state

Electric Potential Energy o If Ui =0, then the final potential energy of the system is Work done to move from infinity

Electric Potential Energy o Example: Near Earth’s surface the electric field has the magnitude E=150 N/C and is directed downward. What is the change ΔU in the electric potential energy of a released electron when the electrostatic force causes it to move vertically upward through a distance d = 520 m?

Electric Potential Energy

Electric Potential Energy Given: Calculation: Eqn:

? ? ? In the figure, a proton moves from point i to point f in a uniform electric field directed as shown. (a) Does the electric field do positive or negative work on the proton? (b) Does the electric potential energy of the proton increase or decrease?

Electric Potential o o It is useful to define the electric potential (or potential) V Units J/C = V (1 volt)

Electric Potential o The electric potential difference between two points i and f is

Electric Potential o Suppose we must apply a force to move a particle in an electric field from point i to point f, then the work done by the applied force is

? ? ? We move a proton from point i to point f in a uniform electric field. (a) Does our force do positive or negative work? (b) Does the proton move to a point of higher or lower potential?

Equipotential Surfaces o Adjacent points that have the same electric potential form an equipotential surface.

Equipotential Surfaces

Potentials and Fields o If I only have the electric field how do I get the potential?

Potentials and Fields o We take the line integral (a particular path) between two points i and f. Here choose Vi as the reference point

Potentials and Fields

? ? ? o For a family of equipotential surfaces and five paths of an electron, (a) what is the direction of the E field for the surfaces, (b) for each path, is the work +, -, or 0, (c) rank the paths according to work, greatest first.

Electric Potential Energy o Sometimes (not always) we will take the reference position (U=0) for a system of charged particles to be when all the particles are infinitely far away.

Electric Potential Energy Ui=0 Uf

Electric Potential Energy o If Ui =0, then the final potential energy of the system is Work done to move from infinity