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: