Chapter 25

 

This chapter introduces charges, insulators, conductors, and an atomic model that can explain many of the observations.  Many smart people did many experiments that lead to the following conclusions:

 

1.         There are two kinds of charges, positive and negative.

2.         Like charges repel one another and unlike charges attract one another.

3.         The magnitude of the force gets smaller the further away the charges are from one another.

4.         There are objects that charges can move through – conductors.

5.         There are objects that charges cannot move through – insulators.

6.         An atom consists of a positive nucleus consisting of protons and neutrons.  The protons have a positive charge and the neutrons have no charge.  The protons in an atom are very strongly bound to the nucleus.

7.         The positive nucleus is surrounded by a cloud of electrons which carry a negative charge.  The number of electrons in an atom is exactly equal to the number of protons in the nucleus.

8.         The charge of a single proton, +e, is -exactly equal in magnitude to the charge of a single electron, -e.

9.         Under normal conditions, most objects have an equal number of positive and negatives charges and are consequently neutral, that is the net charge is zero.

10.       Rubbing an object can either add electrons making the object negative or remove electrons making the object positive.  It is the movement of electrons on or off an object that determines the charge of the object.

11.       The net charge on a conductor resides on the surface of the conductor.  This is because the charges are mobile and like charges repel.  Therefore the excess charges get “pushed” to the surface, as far from one another as possible.

12.       The excess charges on an insulator are immobile and there distribution depends on the details of the method used to charge the insulator.

13.       Because of all the water in our bodies, we are good conductors.  Consequently charges can move through us to the “ground.”  Touching a charged object will typically cause it to discharge.

14.       A charged object will attract a neutral object because of polarization.  For example, a positively charged rod held near a neutral object will attract negative charges and repel positive charges.  The net result is that the charges in the neutral object separate with the negative charges ending up closer to the positive rod and the positive charges end up further from the rod.  Consequently the opposite charges are closer together than the like charges leading to a net attractive force.

15.       Polarization in conductors involve the actual motion of charges while polarization in insulators involves a reorientation of the electron clouds surrounding the materials atoms or molecules.

16.       Coulomb’s Law quantifies many of the observations above.  Coulomb’s law states that the force between two point charges is proportional to the product of the two charges and is inversely proportional to the distance between the charges.  The force is attractive if the charges are opposite and is repulsive if the charges are the same.  The direction of the force is along the line connecting the two charges.  This clumsy word description can be neatly summarized by the equations,

 

F = kq1q2/d2 or F = (1/4πε0)q1q2/d2, where the second form of Coulomb’s law in terms of ε0 will turn out to be more convenient.

 

k = 9 x 109 N m2/C2 and ε0 = 8.85 x 10-12 C2/N m2 where C stands for Coulomb, the standard unit of charge.  In Coulomb’s, e = 1.6 x 10-19 C.

17.       Instead of thinking in terms of the charges exerting a force on one another, we will introduce the concept of the Electric Field, E.  Charges produce an Electric Field (the field is a vector quantity with magnitude and direction) and any other charge situated in that field feels a force qE.

18.       Most of what is needed to know about Electric Fields can be deduced from the following simple model.  The electric field lines due to a positive point charge point radially away from the charge.  The strength of the Electric Field is proportional to the number of lines per unit area that “pierce” an area element perpendicular to the field line.  The field around a negative point charge is exactly the same except now the lines point toward the charge instead of away from the charge.  The field concept was introduced primarily to eliminate the problems with forces acting “instantaneously” across potentially vast distances.

19.       The electric field around a point charge Q can be written succinctly as,

 

            E = (1/4πε0)Q r/r2,

 

where r is a UNIT VECTOR pointing in the direction of increasing r.  (Normally I write unit vectors with a little hat (^) over them but my computer skills don’t include the ability to put the hat over r!)

20.       To reinforce the notion that the electric field is a “local” quantity that has a value anyplace in space, we define the local field as, E = F/Δq, where Δq is a small charge.  More precisely the definition gives the actual field only in the limit that Δq goes to zero, but Δq only has to be small enough to not change the field at the point of interest.  The nice thing about this definition is that we do not need to know anything about the size or location of the charges causing the field at the point of interest.

 

Now work through some exercises and problems before working on the five assigned problems for Chapter 25:  30, 36, 46, 60, 66