ADDITIONS TO Y&F PROBLEMS AND PROBLEMS FROM OTHER TEXTS
                               
                             JULY 31 - AUG 7
        

         YOUNG 11e - CHAPTER 24
         32.  A parallel-plate, air-filled capacitor has plates of
              area 0.00260 square meters.  The magnitude of charge
              on each plate is 8.20 pC, and the potential difference
              between the plates is 2.40 V.  What is the electric
              field energy density in the volume between the plates?

         FISHBANE PROBLEMS - CHAPTER 28
         57.  Show how to use Kirchhoff's loop rule (write a clear and
              concise explanation for each term) to find a differential 
              equation which can be solved for Q(t), the charge as a 
              function of time, on a discharging capacitor.  The figure for 
              this problem is Fig. 26.23 (page 898), with an initial charge   <== misprint here
              of Q_0 on capacitor C when the switch is closed at t = 0.         corrected on 8/01
              Let positive current represent a charging capacitor, i.e. 
              i = (dQ/dt).  Show BY DIRECT SUBSTITUTION that 
              Q(t) = (Q_0)e^(-t/RC) is a solution of your differential 
              equation.

         Halliday and Resnick - 2nd Ed - CHAPTER 29
         22.  An initially uncharged capacitor C is fully charged by a
              device of constant EMF in series with a resistor R.  
              (a) Show that the final energy stored in the capacitor is 
              half the energy supplied by the EMF device.  (b) By direct 
              integration of (i^2)R over the charging time, show that the 
              thermal energy dissipated by the resistor is also half the 
              energy supplied by the EMF device.

         YOUNG 11e - CHAPTER 30
         18.  An air-filled toroidal solenoid has 600 turns and a mean
              radius of 6.90 cm.  Each winding has a cross-sectional area
              of 0.0350 square cm.  Assume that the magnetic field is
              uniform over the cross section of the windings.
              (a) When the current in the solenoid is 2.50 A, what is the
              magnetic field within the solenoid?  (b) Calculate the
              energy density in the solenoid directly from the magnetic
              field strength.  (c) What is the total volume enclosed by
              the windings?  (d) Use the volume from part c and the
              energy density from part b to calculate the total energy
              stored in the solenoid.  (e) Use the geometry of the 
              solenoid to calculate its inductance.  (f) Use 0.5LI^2
              to calculate the energy stored in the solenoid.  Compare
              your answer to what you obtained in part d.

         66.  The figure for this problem is here.  Switch S is closed
              at time t=0 with no charge initially on the capacitor.  
              (a) What is the reading of each meter just after S is closed?  
              (b) What does each meter read long after S is closed?  
              (c) What is the maximum charge on the capacitor and when does 
              it occur?  Here is a pdf version of the same figure.

         68.  The figure for this problem is here.  The capacitor is  
              originally uncharged.  The switch starts in the open position
              and is then flipped to position 1 for 0.500 s.  It is then
              flipped to position 2 and left there.  (a) If the resistance
              r is very small, what is the upper limit for the amount of
              charge the capacitor could receive?  (b) Even if r is very
              small, how much electrical energy will be dissipated in it?
              (c) Sketch a graph showing the reading of the ammeter as a
              function of time after the switch is in position 2, assuming
              that r is very small and that current from left to right 
              through the ammeter is positive. (d) Sketch a graph showing
              the charge on the right-hand plate of the capacitor as a
              function of time after the switch is in position 2, assuming
              that r is very small.  Here is a pdf version of the 
              same figure.

         Young and Freedman - 12th Ed - CHAPTER 30
         68.  When making the graph for part (c), you may use T for the
              period of the oscillations.  Tomorrow you will learn how
              to calculate T in seconds for such a circuit.

         YOUNG 11e - CHAPTER 31
         60.  You enjoy listening to KONG-FM, which broadcasts at 94.1 MHz.
              You destest listening to KRUD-FM, which broadcasts at 94.0 MHz.
              You live the same distance from both stations and both
              transmitters are equally powerful, so both radio signals
              produce the same 1.0 V source voltage as measured at your
              house.  Your goal is to design an LRC radio circuit with
              the following properties: i) It gives the maximum power
              response to the signal from KONG-FM; ii) the average power
              delivered to the resistor in response to KRUD-FM is 1.00%
              of the average power in response to KONG-FM.  This limits
              the power received from the unwanted station, making it
              inaudible.  You are required to use an inductor with
              L = 1.00 microH.  Find the capacitance C and resistance
              R that satisfy the design requirements.  NOTE: To get R, 
              you will need to save C in your calculator and use that 
              saved answer; this is because R depends on the small 
              DIFFERENCE between X_C and X_L, which magnifies any 
              rounding error in X_C. GBA


         Young and Freedman - 12th Ed - CHAPTER 31
         36.  Please add the following parts:
              (d) Assume the circuit elements are arranged as shown 
              in Figure 31.25 on page 1088.  What are the readings
              from voltmeters V4 and V5?  Remember that AC meters
              give RMS values, not peak values. (e) If the
              circuit elements are not changed but the angular
              frequency of the source is changed to 645 rad/s,
              what are the readings on the five voltmeters,
              V1-V5? (f) Repeat part e. for 1245 rad/s.
              
         39.  All the voltage and current values in this question
              are RMS values.  The answers to (b) and (c) in the
              back of the book are wrong (in at least some copies
              of the textbook); the right answers are on our
              even-numbered answers page.

         (P prefixes) HRW Problem Supplement #1 - CHAPTER 32
         28.  Suppose that a parallel-plate capacitor has circular plates
              with radius R = 30 mm and a plate separation of 5.0 mm.
              Suppose also that sinusoidal potential difference with a 
              maximum value of 150 V and a frequency of 60 Hz is applied
              across the plates; that is V = (150 V)sin[2pi(60 Hz)t].
              (a) Find B_max(R), the maximum value of the induced magnetic
                  field that occurs at r = R.  
              (b) Plot B_max(r) for 0 < r < 10 cm.

         38.  A capacitor with parallel circular plates of radius R is
              discharging via a current of 12.0 A.  Consider a loop of 
              radius R/3 that is centered on the central axis between the
              plates.  (a) How much displacement current is encircled by 
              the loop?  The maximum induced magnetic field has a magnitude
              of 12.0 mT.  (b)  At what radial distance, or distances, from 
              the central axis of the plate is the magnitude of the induced 
              magnetic field 3.00 mT?

         Young and Freedman - 12th Ed - CHAPTER 32
         49.  Hint for Problem 32.49: This is a Faraday's Law problem, but 
              with a radiated B field that is varying sinusoidally (so you 
              can write B(t) as Bmax*sin(omega*t) and differentiate to get 
              the maximum value of dB/dt).

         Halliday and Resnick - 2nd Ed - CHAPTER 33
         11.  A coil with an inductance of 2.0 H and a resistance of
              10 Ohms is suddenly connected to a resistanceless battery
              with EMF = 100 V.  At 0.10 s after the connection is made, 
              what are the rates at which (a) energy is being stored in 
              the magnetic field, (b) thermal energy is appearing in the
              resistance, and (c) energy is being delivered by the battery?

         12.  The figure for this problem is Figure 30.11 on page 1041 with 
              EMF = 10.0 V, R = 6.70 Ohms, and L = 5.50 H.  With S2 open,
              S1 was closed at time t = 0.  (a) How much energy is
              delivered by the battery during the first 2.00 s?  (b) How
              much of this energy is stored in the magnetic field of
              the inductor?  (c) How much of this energy is dissipated
              in the resistor?

         FISHBANE PROBLEMS - CHAPTER 33
         46.  The figure for this problem is Fig. 30.11.  After being 
              closed for a long time, S1 is suddenly opened while, at
              the same instant, S2 is suddenly closed.  Show how to
              use Kirchhoff's loop rule to find the differential equation 
              which can be solved for the resulting I(t), and show that 
              I(t) = (EMF/R)e^(-tR/L) is a solution of that differential 
              equation.

         (P prefixes) HRW Problem Supplement #1 - CHAPTER 33
          5.  The frequency of oscillation of a certain LC circuit is
              200 kHz.  At time t = 0, plate A of the capacitor has maximum
              positive charge.  At what times t > 0 will (a) plate A again
              have maximum positive charge, (b) the other plate of the
              capacitor have maximum positive charge, and (c) the inductor
              have maximum magnetic field?

         12.  In an oscillating LC circuit in which C = 4.00 microF, the
              maximum potential difference across the capacitor during
              the oscillations is 1.50 V and the maximum current through
              the inductor is 50.0 mA.  (a) What is the inductance L?
              (b)  What is the frequency of the oscillations?  (c) How
              much time is required for the charge on the capacitor to
              rise from zero to its maximum value?

         44.  An AC generator with EMF_max = 220 V and operating at
              400 Hz causes oscillations is a series RLC circuit having
              R = 220 Ohms, L = 150 mH, and C = 24.0 microF.  Find (a)
              the capacitive reactance X_C, (b) the impedance Z, and (c)
              the current amplitude I.  A second capacitor of the same
              capacitance is then connected in series with the other
              components.  Determine whether the values of (d) X_C,
              (e) Z, and (f) I increase, decrease, or remain the same.

         50.  An AC voltmeter with large impedance is connected in turn
              across the inductor, the capacitor, and the resistor in a
              series circuit having an alternating EMF of 100 V (rms);
              it gives the same reading in volts in each case.  What is
              the reading?  (To get any credit for your answer to this 
              problem, you must very carefully explain the logic that
              you used to obtain that answer.)

         WOLFSON - CHAPTER 34
          6.  An electric field points into the page and occupies a 
              circular region of radius 1.0 m.  There is a magnetic field 
              forming circular closed loops centered on the circular region 
              and pointing clockwise.  The magnetic field strength 50 cm 
              from the center of the region is 2.0 microT.  (a) What is the 
              rate of change of the electric field?  (b) Is the electric 
              field increasing or decreasing?

         20.  What are the wavelengths of (a) a 100 MHz FM radio wave,
              (b) a 3.0 GHz radar wave, (c) a 6.0 x 10^14 Hz light wave,
              and (d) a 1.0 x 10^18 Hz X ray?

         (P prefixes) HRW Problem Supplement #1 - CHAPTER 34
          6.  The figure for this problem is here.  What is the wavelength
              of the electromagnetic wave emitted by the oscillator-antenna 
              system in the figure if L = 0.253 microH and C = 25.0 pF?  
              Here is a pdf version of the same figure.

         40.  At a beach the light is generally partially polarized owing
              to reflections off sand and water.  At a particular beach 
              on a particular day near sundown, the horizontal component
              of the electric field vector is 2.3 times the vertical
              component.  A standing sunbather puts on polarizing
              sunglasses; the glasses eliminate the horizontal field
              component.  (a) What fraction of the light intensity
              received before the glasses were put on now reaches the
              sunbather's eyes?  (b) The sunbather, still wearing the 
              glasses, lies on his side.  What fraction of the light
              intensity received before the glassse were put on now
              reaches his eyes?

         KNIGHT 2nd Ed - CHAPTER 35
         24.  A polarized sinuosoidal radio wave of frequency 1.0 MHz is 
              traveling in the negative z direction.  The electric field of 
              the radio wave oscillates in the plus or minus y direction.
              The maximum electric field strength is 1000 V/m.  What are
              (a) the maximum radiated magnetic field strength,
              (b) the radiated magnetic field strength and direction 
                  at a point where the radiated electric field is
                  500 V/m in the negative y direction, and
              (c) the smallest distance between a point on the wave
                  having the magnetic field of part b and a point where
                  the magnetic field is at maximum strength?

         Halliday and Resnick - 2nd Ed - CHAPTER 36
         NOTE: You are to do parts (a)-(c) of problems 1 and 2 for Aug 4,
               and then part (d) of both problems on Aug 5.

          1.  An AC generator has EMF = (EMF_max)sin((w_d)t), with
              EMF_max = 25.0 V and w_d = 377 rad/s (w stands for omega).
              It is connected to a 12.7 H inductor.  (a) What is the
              maximum value of the current?  (b) When the current is
              a maximum, what is the EMF of the generator?  (c) When the
              EMF of the generator is -12.5 V and increasing in magnitude,
              what is the current?  (d) For the conditions of part (c), is
              the generator supplying or taking energy from the circuit?

          2.  The AC generator of problem 1 is connected to a 4.15 microF
              capacitor.  (a) What is the maximum value of the current?
              (b) When the current is a maximum, what is the EMF of the
              generator?  (c) When the EMF of the generator is -12.5 V
              and increasing in magnitude, what is the current?  (d) For
              the conditions of part (c), is the generator supplying or
              taking energy from the circuit?

          4.  A 50 Ohm resistor is connected to an AC generator with
              EMF_max = 30.0 V.  What is the amplitude of the resulting
              alternating current if the frequency of the EMF is
              (a) 1.00 kHz and (b) 8.00 kHz?

         17.  A typical "light dimmer" used to dim the stage lights in a
              theater consists of a variable inductor L (the inductance
              of which is adjustable between zero and L_{max}) connected
              in series with a lightbulb (a lightbulb is a non-ohmic
              resistor, but assume it is ohmic for the purpose of this
              problem).  The electrical supply for this series circuit is
              120 V (rms) at 60.0 Hz; the lightbulb is rated as "120 V,
              1000 W".  (a) What L_{max} is required if the rate of energy
              dissipation in the lightbulb is to be varied by a factor of
              five from its upper limit of 1000 W?  (b) Could one use a
              variable resistor (adjustable between zero and R_{max})
              instead of an inductor?  If so, what R_{max} is required?
              Why isn't this done?

         KNIGHT 2nd Ed - CHAPTER 36
         67.  The figure for this problem is here.  The figure shows
              voltage and current graphs for a series LRC circuit with a
              generator.  The voltage curve first crosses the time axis
              at t=25 microseconds; the current curve first crosses the
              time axis at t=41.67 microseconds.  (a) What is the
              resistance in the circuit?  (b) If L=200 microH, what is
              the capacitance in the circuit?  (c) What is the resonant
              angular frequency for the circuit?  Here is a pdf 
              version of the same figure.

         
         G1 and G2:
         The differential equation for an undriven LRC circuit is

           (q/C) + R(dq/dt) + L(d^2q/dt^2) = 0    Eq (1)

         Your task is to show that

            q(t) = (Q_0)e^(-(alpha)t)cos((omega)t)

         is a solution of this differential equation, where Q_0, alpha,
         and omega are constants.

         G1.  Substitution of q(t) in Eq (1) gives terms in sin((omega)t) 
              and terms in cos((omega)t).  Show that the sin((omega)t) terms 
              sum to zero only if alpha = R/2L.

         G2.  Show that the cos((omega)t) terms sum to zero only if

                 omega^2 = omega0^2 - alpha^2 where omega0^2 = 1/LC.