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Phys208Honors: Final Exam. December 17, 2002
This is a closed book exam: the formula sheets provided are the only supplemental
materials permitted on this exam.
Programmable calculators and graphing calculators may be used during this exam, but
not for storage of additional notes or formulas.
Show ALL work on problem sheet and only on that sheet.
Please read questions carefully.
Credit may be lost inadvertently if solutions are not neat and orderly.
Be careful with units and signs.
_______________________
1. Answer following questions. Briefly justify all answers (30 pts)
1) (3pt) What is the resistance of an air dryer rated 1000W?
P
V2
,
R
R
V 2 120 2

 14.4
P 1000
2) (3pt) Consider a velocity selector that consists of perpendicular, uniform electric and
magnetic fields, with the B field directed straight up. A beam of positively charged
particles passing through the velocity selector from left to right is undeflected by the
fields. In which direction is the electric field?
E: From the bottom to top.
3) (3pt) What is the electric field halfway to the center of a conducting sphere charged to
a potential of 15 V? What is the potential halfway to the center?
E=0, V=15V
4) (4 pt) Draw a phasor diagram with two ac quantities, V(t)=Vmsin(wt+10),
i(t)=Imsin(wt-40), at t=0 and an arbitrary t.
5) (4 pts) List all the facts for a series RLC circuit at resonance.
1.
2.
3.
4.
I is a maximum
Z is at minimum; Z=R; Z is purely resistive
XL=XC; inductive reactance cancels capacitive reactance; net reactance is zero
The phase angle is zero; the current is perfectly in phase with applied emf; the
tangent of the phase angle is zero.
5. The driven frequency is identical to the natural frequency.
6. The power factor is unity
6) (3pt) As shown in the right figure, a conduction rod is sliding on an insulating rail.
What quantity is induced in the loop?
emf
7) (10 Points) Which of the following statements are correct regarding a capacitor and
inductor?
a)
Current leads voltage in a capacitor. T
b)
No sudden change in current is allowed in a capacitor. F
c)
An inductor behaves like a short circuit in a DC circuit when it reaches steady
state. T
d)
The power dissipated on an inductor is P=i2XL or P=V2/XL. F
2. (20 points) The spherical capacitor is often considered because it is finite-sized but
without the complication of a fringing field, present for the parallel-plate capacitor
usually considered. Find an expression for its capacitance.
a. Use Gauss's law to determine the electric field at a
point between the two conducting shells when
oppositely charged. Be sure to show the gaussian
surface used and indicate the direction of the resulting
field.
b. Evaluate the capacitance.
c. A simple check of your true understanding of
conductors and Gauss's law:
If identical charges are deposited on both conductors, say +1 microcoulombs, how are the
charges distributed among the four surfaces?
#1, inner surface
#1, outer surface
#2, inner surface
#2, outer surface
a) E=kq/r2
1 1
V   Edr  kq  
b c
b
b)
q
1
C 
V
1 1
k  
b c
c
c)
#1, inner surface: 0
#1, outer surface: +1 mC
#2, inner surface: -1 mC
#2, outer surface: +2 mC
3. (20pts) Consider the circuit shown.
a) What is the emf of battery 1?
b) What is the terminal voltage of battery 2?
c) What is the power dissipated by the 12 ohm
resistor?
d) What is the power supplied by the emf of
battery 1?
i1 r1   1  i1 R1  i2 R2   2  i2 r2  0
(a): i1 r1   1  i1 R1  i3 R3  0
i1  i2  i3
  1  i2 ( R2  r2 )  i1 (r1  R1 )   2
  1  i3 R3  i1 (r1  R1 )
i2  i3  i1
  1  6i2  0i3  16
  1  0i2  12i3  8
0 1  i2  i3  2
 16 6 0
 8 0 12
1 
2
1
1 6 0
 1 0 12
0
i2 
1
1
0
1
0
12
1
1 6
144  48  192
 21.3V
12  6
1
 1  16
8
2

0

8  24  16
 0.89( A)
12  6
 1 0 12
0 1 1
i3  1.11( A)
b) Vab   2  i2 r2  9.98(V )
c) P  i32 R3  1.112  12  14.79(W )
d ) P  i1  1  32(W )
4. (15 points). Calculate the magnetic field in terms of current inside of a solenoid
which has a length L=10 cm, total coil turns N=1000, and cross sectional area A=0.01 m 2.
To physically measure the field, one often puts a pick coil inside the solenoid and
measures inductive voltage. The dimensions of the pick up coils are L1 =1 cm, N1
=10000, and cross sectional area A=10-4 m2. Assuming current is increased from 0 to 1
(A) in 0.1 sec, calculate the magnetic field and inductive voltage. (Show your work).
b
 B  ds  B
ab
c
d
a
b
c
d
 ds   Bbc  ds   Bcd  ds   Bda  ds
a
b
b
a
a
Bh   0inh
 Bab  ds  B ds  Bh
B   0in
   0 ni  AN1
d
di
1000
1
V
  0 nAN1   4  10 7 
 10 4  10000 
 0.13V
dt
dt
0.1
0.1
5. (15 points) A metal wire of mass m slides without friction on two horizontal rails
spaced a distance d apart, as shown in the figure. The track lies in a vertical uniform
magnetic field B. There is a current i generated by a source G, along one rail, across the
wire, and back down the other rail.
B
a) Describe what happens starting from t=0.
b) Find the terminal velocity of the metal wire.
(note: you can neglect the force on the metal wire due to the
current in the horizontal rail since the current is small, i.e. it is
not a rail gun).
a) The current i in the wire (from the source G) is sitting in the magnetic field B,
resulting in force towards the left. The wire is accelerating towards the left. As the
wire starts to move left, a current is induced in the opposite direction and the
induced current is proportional to the velocity, which is increasing. Finally, two
forces are at equilibrium, and the acceleration is zero. The velocity reaches
maximum value, i.e. terminal velocity.
b) FB=idB
Find=i’dB
i'=e/R=Bdv/R
FB=Find
v=iR/dB
G