Updated:  8/31/04

Chapter 17 Electric Potential and Electric Energy:
                            Capacitance

A. Instruction to students:
                          1.) Homework:
                                a) Read carefully all sections except Sections 17-6 and 17-8.
                                       Some students may find it useful to review Section 6-1 in pp146-149.
                                b) Do all examples except 17-4, -6, and -8.
                                c) All multiple choice problems posted             
                          2.) Following formula and constants from Chapters 16 1nd 17 will be given
                               during the exams. Practice how to use and apply them.  
                               WRARNIG:   Units are missing from the formula!
                                        W = qV
                                         E = V/d
                                         Q = CV
                                         C = (epsilon_0) A/d
                                         V = kQ/r
                                         U = (1/2)CV^2
                                          F = kQ_1 Q_2/r^2
                                          F = qE.
                                          k = 9.0x10^9
                                          e = 1.6x10^(-19)
                                          epsilon_0 = 8.9 x 10^(-12)

B. Biomedical (and technological) application:
 Cathode ray tube: TV and computer monitors, oscilloscope;
                                                                                        Section 17-10,   pp518-519. 
                          The electrocardiogram (ECG or EKG);  Section 17-11,   pp493-495.


C. Lectures and study guideline

Electric potential (pp502-505)
The electric potential is different from the potential energy.   It is defined as the potential energy
          per unit charge. The unit of the electric potential is, for example, Joul/C = Volt.
          The potential energy and the electric potential have no absolute magnitude.  The values of
          the potential energy and the electric potential are always the differences. (Between what and
          what?)    Remember (from 100A, Section 16-1) the work-energy theorem (principle):
                Work done on the system = - (the change in the total energy of the system).  
          (Example 17-1)

Electric potential V and electric field E  (p506)   
          In the case of the (+ and -) charged parallel plates separated by the distance d, with the potential
          difference V and with the elctric field between the plate E,
               work done by moving a charge q across V is
                                              W = qV
               work done by E on q is
                                               W = Fd =  qEd    (F = qE from Chapter 16)
                so that
                                                E = V/d.                                          
           (Example 17-2)   This expression tells what the unit of E is; Volt/meter, for example.

Equipotential lines (pp507-508)
Equipotential lines cross the elctric field lines perpendicularly.   As the elecric field lines,
           the equipotential lines are artificially drawn and can be drawn as many as one desires
           (but usually by an equal strength of steps.)  View carefully Figs. 17-5 and -6 together with
           Fig. 17-7.

Electron volt (p508)     
           The electron volt is a unit of energy/work as
                                   W = qV = (1.6x10^(-19) C) (1.0V) = 1.6x10^(-19) J
           Here, 1 Coulomb Volt = 1 Joul.

           Electric potential due to point charges (pp509-511)
           The elctric potential due to a charge Q at a distance r from the charge is           
                                    V = (9.0x10^9 Nm^2/C^2) Q/r
            The sign of the electric potential follows the sign of the chrage.
            (Examples 17-3 and -5)

Capacitance (pp513-514)
            The capacitance C is defined through
                                     Q = C V,
            that is,  the capacity to keep the amount of charge Q (on each plate) for the electric
            potential V (between the plates).  The unit of capacitance is thus Coulomb/Volt, which is
            defined to be Farad (F).
            Q increases as V increases;  C is independent of V and Q, unique to the given system.
            In the case of the charged parallel plates of the area A and the separation d,
                                      C = (epsilon_0) A/d
            Here,                  epsilon_0 = 8.9 x 10^(-12) C^2/Nm^2
            is the permittivity of free space (p482) and is related to the constant in the Coulomb's law
            as
                               k= 9.0x10^9 Nm^2/C^2 = 1/(4 x pi x epsilon_0)
            (Example 17-7)

Storage of electric energy (pp516-517)
            In the case of the parallel plates, each of which has the charge Q,  the energy U stored
            in a capacitor of the capacitance C is given by
                                       U = (1/2)CV^2 = QV/2
            (V is the electric potential difference between the plates.)
            Questions:
                  a) Exactly where in the capacitance the energy is stored?
                  b) Derive the expression of the energy density, Eq. (17-9), using the above equations.
            (Example 17-9)

WARNING
             We now have several new units to apply, which are related to each other.  As noted
              above, you can find the relations among the units by examining how the quantities
              themselves are related to each other.  It is thus vital to be able to use and apply various
formula, as also warned in A-2) above.