Physics 260
FINAL EXAM
MWF 10:10-11:00
Dr. Womble
Name:_______________________________
Instructions: Work ONLY 10 of the 12 problems. Cross-out the problems that you will
not work. NO EXTRA Credit will be given for working more than 10 problems.
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) Write the Maxwell equation which describes how a magnetic field lines do not
diverge from any point in space or converge on any point; that is it implies
that isolated magnetic poles do not exist?
b) Which Maxwell equation relates the electric field, E, to the rate of change of
the magnetic field vector, B?
c) In part b), does the electric field which is created by the changing magnetic
field: converge, diverge, or is shaped similarly to a magnetic field?
d) What is the Maxwell equation which describes how the magnetic field lines
encircle an area through which current is passing or through which the
electric flux is changing?
e) What is the Maxwell equation which describes how electric field lines diverge
from positive charges and converge at negative charges?
2)
A proton moves in a circular orbit of radius 65 cm perpendicular to a uniform
magnetic field of magnitude 0.75 T. Mass of proton=1.7 x 10-27 kg.
a. What is the period of the motion?
b. Find the speed of the proton.
3) What is the electric field (magnitude and direction) in terms of k and charge, q, at
Point P in the diagram below ?
2q
1m
1m
Point P
1m
q
4) Find the value of the integral
 B  ds for the surfaces depicted in the diagram below.
A “x” denotes a current going into the page and a “o” denotes a current going out of the
page. The value of the current is given in terms of “i" and is placed next to its respective
current. Hint: Use only the Ampere portion of the Ampere-Maxwell Equation.
i
X
2i
O
3i
X
2i
O
i
Surface 2
X
i
O
Surface 1
Surface 3
a) Surface 1:
b) Surface 2:
c) Surface 3:
5) An electron moves in a circular orbit about a stationary proton. The centripetal force
is provided by the electrostatic force of attraction between the proton and electron.
The electron has kinetic energy of 2.18 x 10-18 J.
a. What is the speed of the electron?
b. What is the radius of the orbit of the electron? (Hint:
mv 2
Centripetal force =
and KE=1/2 mv2 can be re-written as 2*KE = mv2)
r
6) Two concentric spheres have radii 1.5 m, and 2.5 m. The inner sphere has a surface
charge of -2q, and the outer sphere has a surface charge of 4q. Find in terms of k
1
(=
) and q, the electric field at:
4 0
2.5 m
1.5 m
4q
-2q
Hint:
 
 E  da  E (4r
2
) =qenc/
a) r = 1 m
b) r = 2m
c) r= 3 m
7) The electric potential in a region of space is given by the following function:
V ( x, y, z )  2 x 2  5 yz
where 2 and 5 have appropriate units (i.e. don’t worry about them).
Find the magnitude of the electric field at a point x=2 m, y= 1m, and z= 2 m.
8) 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.)
4
12 V
5V
3
9) Find the currents through each of the resistors shown.
2 
6V
2 
0.2 
2
3 
4
10) The power supply in the circuit below has a linear frequency of 100 Hz:
a) What is the impedance of the circuit? (3pts)
b) What is the phase angle? (3pts)
50 H
1 M
100 pF
c) What is the natural frequency of this circuit? (3pts)
d) Does the current lead or lag the voltage? (1pt)
11) A 6 V battery of negligible internal resistance is used to charge a 2 F capacitor
through a 100  resistor.
a. Find the initial current
b. Find the final charge on the capacitor.
c. Find the time required for the charge to reach 90% of its final value.
12) In the circuit below, the battery has a potential difference of 10V and the five
capacitors each have a capacitance of 10 F.
a. What is the charge on capacitor C1?
b. What is the charge on capacitor C2?
C2
C1
10 V
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