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Physics 2220
Spring 2012
Ben Bromley
EXAM 4
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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
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Exam 4
Ben Bromley
1
Show all work!! Report all numbers to three (3) significant figures.
An RLC circuit is powered by an AC generator.
ε(t) = ε0 cos (ωt) where ε0 = 1687 V, and ω = 388 radians/s
C = 1.34 mF
L = 8.22 mH
R = 1.76 Ω
(a)
[10 pts.] Sketch the phasor diagram for this circuit. Show the potential across each component (ε0, VR, VC, VL) at
a time when the potential across the resistor is aligned with the +x axis (horizontal).
(b)
[10 pts.] Find the average power, Pavg, that is dissipated through the resistor.
(c)
[10 pts.] Find the frequency ωmax at which the average power is a maximum.
Physics2220
2220 Fall 2009
Physics
Spring 2012
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
Exam 4
Ben Bromley
2
Show all work!! Report all numbers to three (3) significant figures.
[30 pts.] A current i(t) = I exp(-t/T), where I and T are constants, flows through a capacitor. The capacitor has plates that
are circular and parallel with separation d and radius R. Find an expression for the strength of the magnetic field as a
function of time, B(t), inside the capacitor at a distance r = R/2 from its axis.
Physics2220
2220
Physics
Spring 2012
Fall 2009
Ben Bromley
Name: __________________________________
Unid: ___________________________________
Discussion TA: ___________________________
3
Exam 4
Show all work!! Report all numbers to three (3) significant figures.
Plane wave electromagnetic radiation from the Sun travels in the +x direction, and has a wavelength of  = 623 nm and an
intensity Savg of 1050 W/m2. Find the following quantities.
(a)
[10 pts.] The frequency, f, of the plane wave: f = ______________
(b)
[10 pts.] An expression for the variation in space (x) and time (t) of the magnetic field strength, B(x,t), assuming
that the field has a maximum at x = 0 m and t = 0 s: B(x,t) = ________________________________________
(c)
[10 pts.] The maximum electric force FE exerted on an electron by the plane wave: FE = ______________
(d)
[10 pts.] Radiation pressure Prad felt by an object basking in the sunlight: Prad =
_____________