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Physics 2220
Spring 2012
Ben Bromley
EXAM 2
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Name (signed):
Student ID Number
Discussion Instructor:
U __ __ __ __ __ __ __
Chad
Jon Paul
Maria
Peter
Physics 2220
Spring 2012
Ben Bromley
Data: Use these constants (where it states, for example, 1 ft, the 1 is exact for significant figure purposes).
1 ft = 12 in (exact)
1 m = 3.28 ft
1 mile = 5280 ft (exact)

x


x 2  a 2 dx 
1
3

x2  a2

3
1 hour = 3600 sec = 60 min (exact)
1 day = 24 hr (exact)
2
2
gearth = 9.80 m/s = 32.2 ft/s
gmoon = 1.67 m/s2 = 5.48 ft/s2






dx
 x2  a2 
3

x
a2 x2  a2
1 year = 365.25 days
  ax
e
dx


1 kg = 0.0685 slug
1 N = 0.225 pound
1 horsepower = 550 ft‫ڄ‬pounds/s (exact)
24
Mearth = 5.98 × 10 kg
Rearth = 6.38 × 103 km






Msun = 1.99 × 1030 kg





Rsun = 6.96 × 108 m
22
Mmoon = 7.35 × 10 kg
Rmoon = 1.74 × 103 km
G = 6.67 × 10-11 N‫ڄ‬m2/kg2
9
2
2
k = 8.99 × 10 N‫ڄ‬m /C





εo = 8.85 × 10-12 F/m
eelectron charge = -1.60 × 10-19 C
melectron = 9.11 × 10-31 kg





μo = 4π × 10-7 T‫ڄ‬m/A (exact)
N(Avogadro's No.) = 6.02 × 1023 atoms/gm‫ڄ‬mole
26
= 6.02 × 10 atoms/kg‫ڄ‬mole
cos(a ± b) = cos a cos b ‫ ט‬a sin b
xdx
 x2  a 
2 3/2
xdx
a2  x2

1
x2  a2
  a2  x2
dx
 n  x  x 2  a 2 


x2  a2
1  a  x 2  a 2
  n
a 
x
x x2  a2

dx
x a





x
x
 sin 1   , or  cos 1  
a
a
a2  x2
xdx
2
2
 x2  a2
dx
sin(a ± b) = sin a cos b ± sin b
mproton = 1.67 × 10−27 kg
h = 6.64 × 10-34 J
π = 3.14
8
c = 3.00 × 10 m/s









1 Tesla = 10,000 gauss (exact)
ρ(H2O) = 1000 kg/m3
1
  eax
a









dx
1
 n  a  bx 
a  bx b
dx
 a  bx 2

1
b  a  bx 
Physics2220
2220
Physics
Spring 2012
Fall 2009
Ben Bromley
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Exam 2
1
Show all work!! Report all numbers to three (3) significant figures.
A.

A uniform electric E  4.5iˆ N / C exists in a region of space containing 3 points: O (at the origin),
A (0.4, 0) m and B at (0.4, 0.3 m). Find the change in electric potential ΔVif for the following paths:
ΔVOA ______________________ (path from O to A)
ΔVAB
______________________
ΔVBO
______________________
ΔVloop ______________________ (loop from O to A to B to O)
B.

The electric potential relative to a point at the origin is V(x,y.z) = V1x + V2z2. Find the electric field E (x, y, z).
(Use unit vector ˆi, ˆj, kˆ , as needed).
PhysicsPhysics
2220 2220 Fall 2009
Spring 2012
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Exam 2
Show all work!! Report all numbers to three (3) significant figures.
A.
Two concentric conducting shells have radii a and b (a < b) as shown. The shells may be
treated as if they were a pair of conductors within a single capacitor of capacitance C.
Find C. Must show all work and justify your answer.
B.
For the circuit shown, find I3, the amount of current through the 3 Ω resistor (labeled R3).
ε1 = 6 V; ε2 = 6 V; R1 = 2 Ω; R2 = 2 Ω; R3 = 3 Ω
Ben Bromley
2
Physics2220
2220
Physics
Spring 2012
Fall 2009
Ben Bromley
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Exam 2
3
Show all work!! Report all numbers to three (3) significant figures.
In a model for a thunderstorm, we might view the Earth’s surface and the
lower face of the storm cloud as parallel plates of a capacitor, with
capacitance C = 1.2 μF. The model storm is driven by an emf ε = 2.4 MV
(to account for the energy input from the Sun, and the convection in the
clouds). The system also has some resistance R = 150 MΩ (associated
with moving charges around the system).
(a)
If the surface area of the storm cloud’s lower face is 25 km2 = 2.5 × 107 m2, what is the distance d between the
Earth and the clouds, assuming the system acts like a perfect parallel plate capacitor? d = __________________
(b)
What is the maximum charge Q that can be exchanged between the Earth and clouds in this model?
Q = ___________________
(c)
Find the time T required to build up a voltage ΔVC = 1.2 MV across the capacitor. T = ____________________
(d)
If at some point some amount of charge, q = 0.72 C is able to cut a path between the Earth and cloud (no one
knows exactly how this process works), then lightning strikes. If the lightning bolt is approximated as a uniform
column of charge of length L = 300 m and radius r = 76 mm, flowing at a steady rate for a duration of 30 μs, find
the current density J in the lightning bolt and the total current I.
J = ____________________, I = ____________________