5P222 Section I l2l /3321
12 February 2010
' Name
Exam
\
1
A long non-conducting cylindrical shell has inner radius 0.050 m and outer radius 0.10 m as
shown' The cylinder has-unlform volume charge density' p = +!! pc/m3' use Gauss's Law to
l.
solve for the magriarde of the electric field at a distance r = 0.075
of the shell. (20 Points)
m
(7.5 cm) near the midpoint
For full credit:
Sketch and label the Gaussian surface. (4)
b. Identiff the cbarge inside the Gaussian surface. (6)
dA over the Gaussian surface' (5)
c. Identiff the value of
a
d.
$E
Solve for the magnitude ofthe electric field. (5)
I
b:
l0 cm
2
(o)
Q,,
(r)
fF.di
-P
=.
7-35
{ o.5 */.
=
ZlO oo uf.
Extra credit: In the 1980 Winter Olympics, the USA hockey team defeated a highly favored
USSR team in what was later termed the "miracle on ice." Who coached team USA? (no, it
wasn't really Kurt Russell) (5 points)
Name
Exam
5P222 Section I l2l /3321
12 February 2010
1
2. A charged stick with uniform charge density, 1", is located on the x axis with one end at the
origin. The stick has a length, L as shown on the below diagram. Find an expression for the
electric field at a point on the x-oris at x : -d. (25 points)
For full credit:
a. Draw and label the location and size of a charge element dq. (6)
b. Draw and label the electric field, dE caused by dq. (2)
c. Develop an expression for both dq and dE. (10)
d. Pay attention to the vector nature of dE. (l)
e. Integrate over appropriate limits to determine the electric freld. (6)
v
ey- --d7
---
-+l Fdr,
F
L
-> B)
JI= )dr.
dE -- Eil a
rr
fsu 2
f = l-+'A
l{L >
dp
e*df
z _l.hL=T' d
Ju 2J*
d G,-L)
\-
U
t-* d
f ? kI
f
d
S) ro
Tr+e-
kI
r=.
IL
-..-------\
J
q)
J,^
.
u1
tner
L
d (d rL\
6)
5P222 Section I I2l /3321
12 February 20rc
Name
Exam I
3. A rigid (but massless) meter stick is pivoted about its center as shown. A charge
er :5.00 x l0-' C is placed at one end of the meter stick, and a charge q2: -er is placed a
distance
d:
10.0 cm below
it.
(15 points)
a. What is the torque
b.
on the meter stick about the pivot due to the force between the charges? (10)
What m.Ns hung 25.0 cm from the pivot will keep the meter stick balanced? (5)
J,
dL
50.0 cm
I
-----4:<ii
25.0 cm
a
Fe
e?
?
W:fu'
r"-
's?
0*,o1
u#\ 'nto'' t
l)'
(. I
= ,zz5 N
,la
e.
+
r YF
fTJ = (5'{.225
= , tl3
ItJ= Jr^2
nn-.
=
(rt *Xl .6,yr)
2
f'J'rrn
(rti - (r.qYr")
, lt3 N.rtr _
F,)
_
-
= Frl
,llZ5
Nn1
(vt 0 )
Our Oe ?*ceC
=.lta
,c151
ry
N'P1
Name
Exam
5P222 Section 1 l2l /3321
12 February 2010
1
4.
Two parallel plates are separated by I .0 cm. The electric between the plates is 5.0 N/C as
shown. An alpha particle is released from rest just in front of the positive plate. An alpha particle
is made up of two protons and two neufions. (25 points)
What is the potential difference between
the plates? (3)
- rcfte di
v=
h{
Av = (S -/)(.o, Q 1 ,as v
b.
What is the change in potential energy of
the alpha particle as it travels from the
positive plate to the negative plate? (4)
At{=
1AV=?(srrf,'ecI.osv)
a l.(, f w-b T
c. .What is the kinetic energy of the alpha
particle just before it hits the negative
plate? (3)
V-+2- ['0Fto?oI
lqn
d. What is the velocity
of the alphaparticle just before it strikes the negative plate? (3)
Kr
What is the force on the alpha particle? Include direction.
F 2 1g a
2(,.6 x d,q/)
LeP
(5 ./d
(3)
t3-
=
Z
t
1o YS
r
What is the acceleration of the alpha particle? (3)
g.
Use
C
_--
l-0 rrds P
2.31 |(toa
r\^ ,{ (r.rr-tr ,a l7 ea)
thc acceleration to veri$ you get the same velocity as part d. (3)
^t
Lr_
:
'-
5
lr.
,r" zabt- =)
'"@
-
How long does it take for the alpha particle to travel from one plate to the other? (3)
r.=lnLt - +=E
.J T
=
z 1.or)
Z.its
1.14xro-o 3
t,tob
lrt
zrToYs