Download Exam #1: Physics 3320 - Fall 2023 and more Exams Electromagnetism and Electromagnetic Fields Theory in PDF only on Docsity!
PHYS 33 2 0 Exam #1, Fall 2023 _Your NAME ____________________________
Exam period: 7:30 to 9:00 pm
If you need more space to write, use the back of the pages (or staple extra pages to
the exam). Just BE SURE TO INDICATE CLEARLY that your work is continued,
(and where) if you need more room than the problem page itself.
On my honor, as a University of Colorado at Boulder student, I
have neither given nor received unauthorized assistance on this
work.
Signed, __________________________
1 ) ( 25 points) Consider the `slide rail' shown in
the figure below. You pull the bar that slides
frictionlessly on the u-shaped circuit with
resistance R. The length of the rail is l. A
uniform magnetic field B
points into the page
and fills all space.
(a) ( 9 pts) What is the current in the resistor? What direction does the current flow?
(b) ( 9 pts) What is the external force that is needed to maintain a constant velocity for the
bar? What is the power that this external force provides to move the bar?
c) (7 pts) What is the power consumed by the resistor? How does this power compare with
that in b)?
motioned
EMF
E
ftp.dt
fcixfl.de
for
a
CCW
loop
E
VB l
2
E
YI
t
s
cow
current
14
Fmg
5
51
2131
I
Ip
I
x
feat
e É
ng
P Fear
73,
P 22
43
same
as that
from
b
- (20 pts) Two infinitely long coaxial metal cylindrical shells
of radius a and b ( b > a ), respectively, are separated by weakly
conducting material of conductivity . The electric potential at
the inner and outer cylinders is fixed as V a
and V b
, respectively
with Δ𝑉 = 𝑉 𝑎
𝑏
as the potential difference and V > 0_._
Assume that the current is steady.
(a) ( 8 pts) Solve for the electric potential V ( s ) between the shells (i.e., for 𝑎 ≤ 𝑠 ≤ 𝑏) by
solving Laplace's equation in cylindrical coordinates by direct integration.
(b) ( 3 pts) Find the electric field within the conductor (direction and magnitude).
steady
current
JV
0
stages dat
0
stats
a
Tse's
Vista
ens ta
YEE
IEEE
c
VEa
Ela
C
Va
alma
Vat
lmao
V
en
bla
risk Eugen
strategy
É
or
Ess
Epa's
Because or
so
luba
0
É points
to
s
direction
(c) ( 3 pts) Consider a segment of the cylindrical shells with length l , what is the current
flowing from one shell to the other?
(d) ( 3 pts) What is the resistance between the shells for this segment of length l?
(e) ( 3 pts) Find the power dissipated within the conductor, for the given V and length l.
I
re
IIa's
For
a
segment
with
length
I
s
f
J
di
fit
gifts
sagged
YET
r
g
GE
p
LOV
YET
or
p
FEI
(c) ( 8 pts) Loop 3 which is the same as in part b), is located outside the solenoid, but its center is a
distance d from the central axis of the solenoid ( b ≪ d ). The normal of the loop is parallel to the
solenoid axis. What is the electromotive force generated around the loop? What is the direction of
the induced current (clockwise or counterclockwise viewed from above z axis)? What is the electric
field 𝐸
⃗
(both the magnitude and direction) at the point on the loop that is closest to the central axis of
the solenoid (i.e., at a distance of d-b from the central axis)?
JOE
dt
EZeb Moab's
É
Mbna
9
CW
E
flip
dt
If
For
loop
3
fB
def
o
as
Bono
2
0
no
indued
current
For É
at
a distance
of
d
b
from
the
central
axis
from
a
É
EEE
ow
