Lecture 5:

Potential Energy and Electric Potential (Ch. 19)

03-02-07

Potential Energy

Remember Gravitational Potential Energy from 121?

 

                                         

Electric Potential Energy

As the charge moves from A to B, work is done by the electric force similar to the work done by gravitational force

Electric Potential Difference

The electric potential V at a given point is the electric potential energy EPE of a small test charge q0 situated at that point divided by the charge itself:

SI Unit of Electric Potential: joule/coulomb = volt (V)

Examples 1, 2 3

Electric Potential Difference

Neither the potential V nor the potential energy EPE can be determined in an absolute sense, because only the differences ΔV and ΔEPE are measurable in terms of work WAB.

A positive charge accelerates from a region of higher electric potential toward a region of lower electric potential.

A negative charge accelerates from a region of lower potential toward a region of higher potential.

volt is a unit for measuring electric potential difference.

One electron volt is the magnitude of the amount by which the potential energy of an electron changes when the electron moves through a potential difference of one volt.

Why does the bulb come on as soon as you turn on the switch?

Electric Potential Difference Created by Point Charge

In the limit that rB is infinitely large, the term kq/rB becomes zero, and it is customary to set VB equal to zero.

When two or more charges are present, the potential due to all the charges is obtained by adding together the individual potentials

Equipotential Surfaces & Their Relation to Electric Field

An equipotential surface is a surface on which the electric potential is the same everywhere.

The equipotential surfaces that surround the point charge +q are spherical. The electric force does no work as a charge moves on a path that lies on an equipotential surface, such as the path ABC. However, work is done by the electric force when a charge moves between two equipotential surfaces, as along the path AD.

The net electric force does no work as a charge moves on an equipotential surface.

Problem solving insight: the electric field created by any charge or group of charges is everywhere perpendicular to the associated equipotential surfaces and points in the direction of decreasing potential.

Equipotential Surfaces & Their Relation to Electric Field

The radially directed electric field of a point charge is perpendicular to the spherical equipotential surfaces that surround the charge. The electric field points in the direction of decreasing potential.

Equipotential surfaces (in blue) of an electric dipole. The surfaces are drawn so that at every point they are perpendicular to the electric field lines (in red) of the dipole.

Equipotential Surfaces & Their Relation to Electric Field

Example 9

Capacitance of a Capacitor

Relation between charge and potential difference for a capacitor

The magnitude q of the charge on each plate of a capacitor is directly proportional to the magnitude V of the potential difference between the plates:

where C is the capacitance.SI Unit of Capacitance: coulomb/volt = farad (F)

Dielectric Constant

Dielectric Constant

This reduction in the electric field is described by the dielectric constant , which is the ratio of the field magnitude E0 without the dielectric to the field magnitude E inside the dielectric:

Capacitance of a Parallel Plate Capacitor

                         

Energy stored in a Capacitor

                           

Biomedical Applications of Electrical Potential Difference

                         

                           

Neuron

Biomedical Applications