Physics 260
FINAL EXAM
MWF 10:30-11:30
Dr. Womble
Name:_______________________________
THE MORE WORK SHOWN, THE MORE CREDIT GIVEN!
Constants:
1
k=
= 9 x 109 Nm2/C2
4o
o = 8.85 x 10-12 C2/ Nm2
0 = 4 x 10-7 Tm/A
mass electron, me = 9.11 x 10-31 kg
electron charge, e = -1.6 x 10-19 C
Conversions:
1 eV =1.6 x 10-19 J
Units:
V = J/C ; A= C/s ;  = V/A; F = C/V ; W = J/s ; T= N/(A*m) ; Wb = T*m2 ; H =
T*m2/A
1) Maxwell’s Equations (2 pts each):
a) What is Maxwell equation which describes how a time-varying magnetic field
can create an electric field?
b) Does the electric field of the above equation diverge from a central point or
circulate like a magnetic field?
c) What is the Maxwell equation which says that there are no magnetic
monopoles?
d) What is the Maxwell equation which says that electric monopoles exist?
e) Write the remaining Maxwell equation and give a brief description.
2) A circuit diagram is shown below:
100 
250 V
15 
25 
10 
50 
a) What is the equivalent resistance? (2 pts)
b) What is potential difference across the 10, 50, and 15  resistors? (3 pts)
c) What is the current through each of the resistors? (5 pts)
3) A circuit diagram is shown below:
C2 =F
a) What is equivalent capacitance? (4 pts)
1 F
b) What is charge and the voltage
across the 3 F capacitor (C2)? (3 pts)
2 F
50 V
4 F
C 1 = 5 F
c) What is charge and the voltage across the 5 F capacitor (C1)? (3 pts)
4) Find the currents through each of the resistors below: (Note: 8 pts will be given for the
proper arrangement of the linear equations. Write down your equations in a clear form.)
25 
30 V
75 
50 
5V
12 V
5) The power supply in the circuit below has a linear frequency of 60 Hz:
a) What is the impedance of the circuit? (3pts)
50 mH
b) What is the phase angle? (3pts)
c) What is the natural frequency of this circuit? (3pts)
75 F
d) What condition must be met so that this circuit is in resonance? (1pt)
6) The figure below shows a cross-section of a coaxial cable and gives its radii (a,b,c).
Equal currents i are uniformly distributed in the two conductors and both flow out of
the page. Derive expressions for the magnetic field B(r) for the following regions in:
 
Hint: The left hand side of Ampere’s Law for this geometry is  B  d s  B(2r )
a) r < a (2.5 pts)
a
b) a < r < b (2.5 pts)
c
b
c) b< r <c (2.5 pts)
d) r > c (2.5 pts)
7) In the figure below, an electron of mass m, charge e, and negligible speed enters the
region between two plates of potential difference V and plate separation d, initially
headed toward the higher-potential top plate in the figure. A uniform magnetic field
of magnitude B is directed perpendicular to the plane of the figure. Find the
minimum value of B at which the electron will not strike the top plate.
HINT: For this problem, the kinetic energy, ½ mv2 is equal to eV. And the units of
the electric field are volts per meter!
Higher potential
V
d
Lower potential
8 ) Three concentric spheres have radii 1.5 m, 2.5 m, and 3.5 m. A point charge of
charge q is placed at the center of innermost sphere. The innermost sphere has a surface
charge of -2q, the middle sphere has a surface charge of 4q, and the outermost sphere has
a charge of -8q (see figure below). Find in
1
terms of k (=
) and q, the electric field
40
at:
 
2.5 cm
Hint:  E  da  E (4r 2 ) =qenc/
a) r = 1 m (2.5 points)
1.5 cm
3.5 cm
q
-2q
b) r = 2 m (2.5 points)
4q
-8q
c) r= 3 m (2.5 points)
d) r= 4 m (2.5 points)
9) Four long copper wires are parallel to each other, their crosssections forming the corners of a square with 20-cm sides. A 20 A
current exists in each wire in the direction shown in figure to the
right. What are the magnitude and direction of the magnetic
field, B, at the center of the square?
10)
20 cm
X
20 cm
20 cm
X
20 cm
10) Find the electric potential at point P in terms of k, q and d for the system of four point
charges shown below. Please algebraically simplify answer and round-off answer to
second decimal place.
-1.2 q
3q
1.5 d
3d
4d
4.472 d
5d
-6q
4q
List of Necessary and Unnecessary Equations
q1 q 2
1
1. F =
4 o r
2. F=qE
1 q
r̂
3. E =
4o r 2
F
4. E =
q
2
5.    E  da 
qenc
0
6.  o   qenc

7. E=
o

8. E=
2 o

9. E =
2o r
W
10. V =  
q
f
11. Vf - Vi =   E  ds
i
q
12. V=
4 o r
13.
V=
n
1
Vi 

4o
i 1
V
14. Es= s
1
15. i =
16. R=
17.  

V
i
1

18. R = 
33. Fba= ibLBa
34.  B  dA  0
35.  E  ds  - dB
dt
36.
 B  ds   
0
n
qi
i 1
i
r
J  dA

mv 2
r
21. K = ½ mv2
22. L = mvr
2r
23.T =
v
1
24. f=
T
25. F = q v  B
26. F = i L  B
27. = N i A
 ids  rˆ
28. dB = o
4 r 2
 i
29. B = o
2r
 i
30. B = o
2r
31. B= 0 i n
32.  B  ds   0 ienc
20. Fc =
E
J
L
A
19. P= iV = i2R =
V2
R
0
dE   i
0 enc
dt
37. E= - dB
dt
38. id =  0 dE
dt
39. E = i R
40. q = C V
41. Ceq =  Cj (parallel)
1
42.
=  1 series
Cj
Ceq
j
43. U = q2/ (2C)
44. Req =  Rj (series)
1
45.
= 1
Rj
Req
j
(parallel)
46. C = R*C
47. q = C E (1 – exp
(-t/(RC)))
(charging)
48. i = (E/R) *exp (t/(RC))
(charging)
49. q= qo*exp (-t/(RC))
(discharging)
50. i = -(q0/(RC)) * exp
(-t/(RC))
(discharging)
51. L = (N)/i
52. E = -L di
dt
53. U = ½ Li2
54.  = 1
LC
2
55. Z = R2 + (XL –
XC)2
56. tan  = (XL – XC)/R
57. XL = d * L
58. XC = 1
 dC
59. Irms = Imax / 2
N
60. VS = Vp s
NP
61.  = 2f
62. c = f