Chapter 15  Electric Forces and Electric Fields

15.1 Properties of Electric Charges

•  It is possible to transfer electric charge from one object to another by rubbing. (Static Electricity)

•  Electric charge is an intrinsic property of proton and electrons, only two types of charge have been discovered, positive and negative.

•  I will use a symbol q for a charge.  The unit of charge q, [q], is C (coulomb).

•  The electron carries charge -e and the proton carries charge +e.

          e = 1.60 x 10-19 C

•  The charge on an electron or a proton (e) is the smallest amount of free charge that has been discovered (quantized).  Thus, any charge of magnitude of q is an integer multiple of e; q = Ne.

€ Properties of Electric Charges€

1.     Unlike charges attract one another and like charges repel one another.

2.     Electric charge is always conserved.

3.     Charge is quantized – that is, it exists in discrete packets that are integral multiples of the electronic charge.

4.     The force between charged particles varies as the inverse square of their separation.

15.2 Insulators and Conductors

•  Substances (materials) that readily conduct electric charge are called electrical conductors.  (Metals such as copper, aluminum, silver, and gold)

•  Materials that conduct electric charge poorly are known as electric insulators.  (Dielectrics such as rubber, plastic, and wood)

•  The difference between electrical conductors and insulators is related to atomic structure.

<Charging by Conduction (by touching)>

•  The object being charged in this process is always left with a charge having the same sign as the object doing the charging (Figure 15.3).

<Charging by Inducting (without touching)>

•  When a conductor is connected to Earth by means of a conducting wire, it is said to be grounded.

•  Figure 15.4

15.3 Coulomb’s Law 

€ Coulomb's Law €

The magnitude F of the electrostatic force exerted by one point charge on another point charge is directly proportional to the magnitudes q1 and q2 of the charges and inversely proportional to the square of the distance r between them

F =                                 (15.1)

where ke is a proportionality constant called the Coulomb constant (ke = 8.99 x 109 Nm2/C2).  The electrostatic force is directed along the line joining the charges, and it is attractive if the charges have unlike signs and repulsive if the charges have like signs.

•  The unit of F, [F], is N (newton).

•  Examples


<The Superposition Principle>

•  It is convenient to deal with a three-charges problem in parts.

•  First, find the magnitude and direction of the force exerted on q1 by q2 (12).

•  Second, find the magnitude and direction of the force exerted on q1 by q3 (13).

•  The net force on q1 is the vector sum of these forces.

•  Examples

15.4  The Electric Field

•  Similar to Gravitational force, the electrostatic force (Coulomb force) is capable of acting through space, producing an effect even when there is no physical contact between the objects involved.  Since no physical contact is required for the electrostatic interaction, we assume that there exists an electric field around a charged object.  When another charged object enters this electric field, forces of an electrical nature arise.   

€ Definition of the Electric Field €

The strength of the electric field is defined as the electrostatic force experienced by a small test charge qo placed at that point divided by the charge itself.

|*| || /| qo|                               (15.4)


The electric field is a vector, and its direction is the same as the direction of the force on a positive test charge.

The unit of  is N/C (newton per coulomb).

<Point Charges>

•  The magnitude of the electric field produced by a point charge q is 

          E = ke                        (15.5)

•  At a particular point in space, each of the surrounding charges contributes to the net electric field that exists there.  To determine the net field, it is necessary to obtain the various contributions separately and then find the vector sum of them all.

•  Examples

15.5  Electric Field Lines

•  A convenient aid for visualizing electric field patterns is to draw lines pointing in the direction of the electric field vector at any point. (Electric field lines)

1.      The electric field vector, , is tangent to the electric field line at each point.

2.      The number of lines per unit area through a surface perpendicular to the lines is proportional to the strength of the electric field in a given region.




•  The rules for drawing electric field lines:

1.    The lines must begin on positive charges (or at infinity) and must terminate on negative charges or, in the case of an excess of charge, at infinity.

2.    The number of lines drawn leaving a positive charge or approaching a negative charge is proportional to the magnitude of the charge.

3.    No two field lines can cross each other.

•  See Figures 15.13, 14, 15, and 16.

•  Example

15.6  Conductors in Electrostatic Equilibrium

€ Properties of an isolated conductor €

1.      The electric field is zero everywhere inside the conductor.

2.      Any excess charge on an isolated conductor resides entirely on its surface.

3.      The electric field just outside a charged conductor is perpendicular to the conductor’s surface.

4.      On an irregularly shaped conductor, the charge tends to accumulate at locations where the radius of curvature of the surface is smallest – that is at sharp points.

•  Figure 15.20

•  Example

15.7  The Millikan Oil-Drop Experiment (Reading Assignment)

15.8  The Van De Graaff Generator (Reading Assignment)

15.9  The Oscilloscope (Reading Assignment)

•  Figure 15.24

15.10  Electric Flux and Gauss’s Law (Reading Assignment)

•  The electric flux, FE, is the total electric field line (E) passing through a surface with an area A; FE = EA.  It is an important concept in physics.

•  Figure 15.26