Physics 2020
Spring 2009
Stephan LeBohec
DATA SHEET - EXAM 3
SEAT #
Constants:
k=
1
9
2
−2
=8.99×10 N⋅m ⋅C
4  0
Electric potential:
Work by operator moving a charge in an electric potential: W =q⋅V f −V i 
Electric field in a parallel plate capacitor:
 ∣=  V = 
∣E
d
0
−19
e=1.602×10
C
Q Proton =e & Q Electron=−e
Electric potential from a point charge: V r =k
Capacitance: C=
q
r
q
V
Energy stored in a capacitor:
1
1
1 q2
2
U = q⋅ V = C⋅ V =
2
2
2C
Electric cirduits:
Power in an electric circuit: P=V⋅I
Resistivity:
R=
L
A
Power from harmonic voltage and current:
I0
V0
P=I RMS⋅V RMS with I RMS =
and V RMS=
2
2
Equivalent resistance for resistors in parallel:
1
1 −1
R Parallel =  
R 1 R2
Equivalent capacitance for capacitors in series:
−1
1
1
C Series =  
C1 C 2
Magnetic force:
 ∣=∣q∣⋅∣v∣⋅∣ 
Magnetic force on a charge: ∣F
B∣sin 
Ohm's law: V =R⋅I
Temperature dependence of resistivity:
=0 1T −T 0
Equivalent resistance for resistors in series:
R Series= R1R 2
Kirchhoff's junction rule: ∑ I IN =∑ I OUT
and loop rule: ∑  V UP =∑  V DOWN
Equivalent capacitance for capacitors in parallel
C Parallel =C 1C 2
 ∣=I⋅L∣ 
Magnetic force on a current: ∣F
B∣sin 
Physics 2020
Spring 2009
Stephan LeBohec
EXAM 3
Name:_____________________________________
TA (circle one): Michael
A)
Sarah
Adam
1
Student ID #:___________________________
Isaac
[33 points, 3 points per question] For each statement, circle the option you find appropriate.
You do not need to show your work.
1) The electric field is always perpendicular to an equi-potential surface.
TRUE
FALSE
2) An equi-potential surface can not cross itself.
TRUE
FALSE
3) When an electron moves to a region of higher electric potential, its potential energy decreases.
TRUE
FALSE
4) Two light bulbs connected in series to a battery produce as much light as a single light bulb connected to the
same battery.
TRUE
FALSE
5) A battery can deliver a fixed amount of charge in its life time. Increasing the number of light bulbs
connected in series will make it last
LONGER
THE SAME
SHORTER
6) Increasing the number of light bulbs connected in parallel will make it last
LONGER
THE SAME
SHORTER
7) An electron moves in a straight line through a uniform magnetic field. There must be an electric field pointing
in a direction perpendicular to the magnetic field.
TRUE
FALSE
8) Two same sign electric charges are brought together in a uniform magnetic field. When released the particles
will move away from each other and stay on circular orbits.
TRUE
FALSE
9) An operator moves an electric charge at constant speed along a straight line perpendicular to a uniform
magnetic field. The operation requires an amount of work proportional to the distance traveled.
TRUE
FALSE
10) An electron moves horizontally away from you in a uniform magnetic field pointing to your right. The
trajectory of the electron
BENDS DOWN
REMAINS HORIZONATAL
BENDS UP
11) A proton moves upward vertically in front of you. In order to bend its path away from you, you need to
establish a horizontal magnetic field pointing
TO YOUR LEFT
AWAY FROM YOU
TO YOUR RIGHT
TOWARD YOU
Physics 2020
Spring 2009
Stephan LeBohec
Name:_____________________________________
TA (circle one): Michael
B)
2
EXAM 3
Sarah
Adam
Student ID #:___________________________
Isaac
[15 points] A Wheatstone bridge is a measuring instrument invented in
1833. In the circuit on the right, Rx is an unknown resistance to be measured; R1,=10Ω, R3 =40Ω and the resistance of R2 is
adjustable. R2 is adjusted so VD­VB=0 at which point R2=18Ω. What is the value of Rx ?
Once R 2 is adjusted V D −V C =V B −V C . Suppose the battery V
provides an electromotive force V , then V D −V C =R 2⋅
and
R1R 2
R2
RX
V
V B −V C =R X⋅
=
so or
R 3R X
R1 R2 R3 R X
R R
R 2  R3 R X =R X  R 1R 2 and R 2 R 3=R X R 1 so R X = 2 3 and with the given values we get R1
R X =18×40 / 10 =72
C)
Two charges q 1=1.0 C and q 2=−3.0 C are positioned as
indicated in the figure with w=0.60m and h=0.80m .
1) [10 points] What is the electric potential at point M ?
q1
q2

 and r 1M=  0.6m 20.8m2=1m so
r 1M r 2M
−6
−3×10−6 C
9 1×10 C
V M =9×10 

=−36,000 V
1m
0.6m
V M =k 
2) [10 points] A particle of mass m=6g and charge
placed at point M and is released.
What will be the final velocity of this particle?
q=−3 C is
The negatively charged particle in a negative electric potential has a positive
1
2
potential energy. It will move away to infinity where the potential energy will have dropped to zero so q⋅V M = m v
and
v=

2q⋅V
m
with the given numerical values,
v=

−6
2×3×10 C×36,000V
−1
.
=6 m⋅s
−3
6×10 kg
2
Physics 2020
Spring 2009
Stephan LeBohec
Name:_____________________________________
TA (circle one): Michael
D)
3
EXAM 3
Sarah
Adam
Student ID #:___________________________
Isaac
We consider the circuit in the figure with V 1 =1V , V 2=3V ,
V 3=2V , R1 =10  , R 2=20  and R 3=30  .
1) [6 points] What is the electric potential difference V A−V B ?
V A−V B =−V 1−V 3=−1V−2V=−3V
I1
I2
I3
2) [26 points] What is the total power dissipated in the circuit?
From Kirshhoff's rules:
a) I 1=I 2I 3
b) R1 I 1 R2 I 2 V 1=V 2
combining a) and c) we get d) R 1 I 1R 3  I 1−I 2V 3V 1=0 then we can
c) R 1 I 1R 3 I 3 V 3V 1 =0
rewrite c) and d) as
e) R 1 I 1 / R2 I 2V 1−V 2/ R 2=0
adding up e) and f) we get
f)  R1 R3  I 1 / R 3V 1V 3 / R3 −I 2=0
V 1−V 2 /R 2V 1 V 3 / R 3
R1 / R 2 R 1R 3 /R 3
1V−3V/20 1V2V/30 
=0A .
and with the numerical values we are given I 1=−
10 /20 10 30 /30 
Then from e) I 2=−R1 I 1 / R 2−V 1−V 2 / R 2=−1V−3V/ 20 =0.1A .
Finally from a) we have I 3=I 1−I 2=−0.1A .
R1 I 1 / R2 R1 R3  I 1 / R 3V 1−V 2 /R 2V 1V 3 / R 3=0 from which
The total power dissipated in the circuit is
I 1=−
P=R 1 I 21R 2 I 22R 3 I 23=20 0.1A230 0.1A2=0.5W