17.1. Electric Potential

Electrical Potential Energy

Electrical Potential Energy

Electrical Potential Energy

In a parallel-plate capacitor, a positive charge close to the positive plate has high potential energy, while a positive charge close to the negative plate has low potential energy.

If released from point “a”, the charge will move to point “b”, losing PE and gaining KE.

The field lines indicate how a positive charge will move; they are perpendicular to lines of potential.

Electrical Potential Energy

Electric potential energy can be defined because the electric force in conservative (reversible).

Note that moving a charge along field lines either requires work or releases potential energy, while moving a charge perpendicular to field lines does not.

Electrical Potential = Voltage

Batteries

A battery, by separating electric charge, creates an electric potential (i.e. voltage), which stores electrical potential energy. Since

1 V = 1 J / C

Equivalently

1 J = (1 C) (1 V)

So a 1.5-V battery does 1.5 J of mechanical work for every coulomb of charge that flows across it.

Example 1

Voltage

A high-voltage system has a lot of potential energy. This is created by keeping opposite charges apart, or like charges close together.

A separation of opposite charges produces potential energy. Similarly, an investment of energy (i.e. work) can produce a separation of charges, which stores energy.

Which object has greater potential energy?

Electrical Potential and Capacitors

Electrical Potential and Electric Field

Electric Field is like the slope of a hill

Electric Field and Electric Potential

Example 2

Example 2

Equipotential Lines

An equipotential is a line or surface over which the potential is constant.

Electric field lines are perpendicular to equipotentials.

The surface of a conductor is an equipotential.

Equipotential Lines

The Electron Volt

Energy is conserved in electrical systems

Energy Conservation

Electric Potential for a point charge

Electric Potential Energy for a point charge

Electric Potential Energy for a point charge

For a positive test charge:

Plate Capacitor v.s. Point Charge

Example 3

Electric potentials add linearly

Example 4

A “local” minimum along the x axis.

The Electric Potential of Point Charges

Equipotential Surfaces

For two point charges:

Example 5

Electrocardiograph

There are electric fields inside the human body; the body is not a perfect conductor, so there are also electrical potential differences.

An electrocardiograph plots the electrical

potential difference due to the heart’s electrical activity: