Download Solutions

Indiana University
PHYSICS P222
PRACTICE Exam #1
Multiple Choice Questions
(Choose only one answer and label your answer clearly.)
28 September 2006
1. An electric field is moqt directly related to:
(a) the momentum of a test charge
The exam is a closed-book examination. You may not refer to lecture notas, textbooks, or
any other course materials. You may use a calculator, but solely for the purpose of arithmetic
computation. A list of potentially useful formulas, definitions and relations is given after the
problems.
The &am will consist of five multiple-choice questions, each worth 2 points for a total of
10 points, and twoproblems to be worked out, each worth 10 points. For the two problems,
you must show all work: clearly state and justify any arguments, assumptions, and approximations, as well as the use of any formulas. Unless otherwise specified, evaluate all integrhls
and derivatives, and perfom any arithmetic calculations if a numerical answer is requested.
(b) the kinetic energy'of a test charge
(c) the potential energy of a test charge
A
A
@ the force acting on a test charge
F-
(e) the charge carried by a test charge
%e
=
4..
.E
L
~
~
e b 9 c s st 44yositinn
L
~
~
H
~
&
2. Electric field lines:
(a) are trajectories of a test charge
..
- not
MCCSS-\~
(b) cross each other in the region between two point charges --never
IZ hmg~~t
h C L Iiinc
~
@ indicate the direction of the electric field.
(d) form closed loops that start and end on a point charge
-
(e) are none of the above
-
o p p ~ ; charqcs
+e
Ciwgej%>
3. To make an uncharged object have a positive charge:
end
not s a m e
% new
c ) ~loops
~ sC J
uq\;k
m9nehc
(a) remove some neutrons
p . ~ ~1
(~"LJ 5 b C
k~14'Itbe~)
i
I
I
I
(b) add some neutrons
I
(c) add some electrons
@remove
some electrons
1
(e) connect i t to ground
I
4. Choose the correct statement:
(a) A proton tends to go from a region of low potential to a region of high potential.
I
I
I
0
(b The potential of a negatively charged conductor must be negative relative to zero
potential at infinity.
D
L
E -0
(c) If 2 = 0 at a point P, then V must be zero at P. +%e;-~-~ +y
(d) If V = 0 at a point P, then
(e) none of the above.
-
2 must be zero at P.
d/%
d/c
I
5 . If 500 J of work are required to carry a charged particle between two points with a
potential difference of 20 V, the magnitude of the charge on the particle is
8. A proton p and an electron e are on the x axis. The directions of the electric field at
points 1, 2 and 3 respectively is given by:
(a) 0.04 C
(b) 12.5 C
m 25C
.
L
/
t
3 $ 2S
(d) can not be computed unless the path is given,
(_Vg-
(e) none of the above
qp&FrvmA+B
C.
(4
-7
(d) -,
-
--,, --,
-,
(e) none of the above
6. Three possible configurations for an electron e and a proton p are shown below. Take
the zero of potential to be at infinity and rank the three configurations according to
the potential at S from most negative to most positive.
9. Two uncharged metal spheres, L and M, are in contact. A negatively charged rod is
brought close to L, but not touching it. The two spheres are slightly separated and
the rod is then withdrawn. As a result:
(a) both spheres are neutral
V
(b) both spheres are positive
(c) both spheres are negative
(d) L is negative and M is positive
@ L is positive and M is negative
0
660
Q
@
10. If the electric potential is given by V(x, y) = C, x+Cz y, where C1 and C2 are constants,
which of the following statements is NOT true?
(a) The electric field has components in the x and y directions only
(a) 1, 2, 3
(b) The electric field is uniform (constant in magnitude and directio everywhere).
=
E y = - ~ ~ ; - C i , &=-% =O
~ and
1 E,2 = -c2~ ~ 1 2 .
ax
a*
(b) 3, 2,l
,
@ E, = -4~
( 4 2, 3, 1
@) 1 and2 tie, then 3
ti
(d) The potential difference, (Vg - VA),between two points A at (a = 0, y = 0) and
B
Bat(x=O.~=d)isC2d ~ ~ - v ~ = - ~ ~ i . d ; = - ~ ( - ~ , ~ - ~ ~
(e) 1 and 3 tie, then 2
-
-F
11. An electric.dipole in an external electric field fas the least potential energy when it
7. A positively charged insulating rod is brought close to an object that is suspended by
a string. If the object is attracted toward the rod, we can unambiguously conclude one
of the following:
(a) is parallel to the electric field
@)anti-parallel to the electric field
(a) the object is positively charged
(c) perpendicular to the electric field
(b) the object is negatively charged
(d) experiences no net external force
(e) none of the above
(c) the object is an,insulator
(d) the object is a conductor
@ we do not have enough information to conclude any one of the above
objec,+
k ny 4hvdb
OR 4 " n d
'%"
., T'
~ ~ b
3
LIZ-$.E
3
).@~$)=
' 0
.b~e
=-$I.
-nBin-i
-
. .
Problems
12. In the figure, two small objects carrying net charges +Q and -Q are shown, where Q
is a positive number with units of Coulombs. They me located on the y-axis, separated
by a distance 6d meters, a s shown. Suppose we place a third object with charge +2Q
at the point P given by (x = 4d, y = 3d).
What are the horizontal and vertical components o m e electric f=& felt by this third
object, expressed m terms of Q, d, and en?
r h . - & b i ~ . ~ G ~4_&
~ b t h....
-.c~Yr&.. ~ . y . . L . if- & d . . i n ~ f i k o n . i .
--..@-&A
...
........................
....
!
............
.- c + ~ u . ~ ~ . ~ k ~ ~ . ~ ~ i - . . . ~ b A ~ m.s.,,a... h , ~
:.&.(i-$+ts
'a<@.
I A ) ~L.
..........-.....
.....
....................
.....
..: ..............
..
.....................
----..-p-p---....-..-..
..-.-.-...---...-
I.
.
.
.
.
.
JqS'i'
-dGxf
.
.,-
.....
..-.
.-
%....
-.- -.
..........
. . .
.
-
.--
-
..
-2L
...&.
Lb0hrn
nR
( 2 R)
~-..
........
...................
_
........
,
.-..-
.....
--
i
..
.........
.,
... -
R2
2
--
'
A P
-:
l - & & ~ * k dv
U
,
P?
__
.................
...
.-....
-1?
.
-..
'
bd % w , ~ f
R' ;
...
.
. - ......................
..-..-.....
2
.... - ...............
..
.-
-
-~-
.........
.
as a
.
.......
.*
.................
.............
w r\nr\n+,-.-.d."$j _.
9-i
&4&
-- ---.- ..- ..-...
I
-., .-
.- -
.
.....
-
...
.
_.
.
. . . . . . . . .
.
...
. .
................................
.....................
..J
--.-
.............................
- .... -..-..... -. .. .- -..
..- .
=. .-.t..d...&bf
?' .
- ........~.~...&~~~..&.......~~~.........
.. . .
( ~ - & - - ~ . . - : & i k _ ~ . i a \ . - . w . + - ..&,k...c.hp.ul.k.
-6,r,.t.:@..@_axii...
b
:-kc&
,
n t f'
-s i
. , L ~ i ~ ~ ~ ~ i ~ ~ : + ~ , . ~ . ~ ~&.)L~lL~-h.JY
. , ~ l i . . k ~ ~
m . ~ h &AL
r
n~ed$
-
......................................................
A h . ,-. &
.-.- .....-..--...
.
. . . .
a-.
. . , ,-
-L
&*,LI&J&_-.-
.-
...........-..
- ...............................
.................
~..+~**.f"-d..+
................
&.:.
=- + Q
=...A&-:
..................................
Lhp
f(irrR)
TR
.
.
._
.....
1 _
__
.
......................
-_
_-
__ .
_
--.-
=
&p.
. . .
.....
.......
..
P ....
.
3
.- ..
.......................
ds
= a'.-RdeL-Tde
.L-&
.....
........
.
.....
.............
14. In the figure, a non-conducting rod of length L has charge q uniformly distributed
along its length. Find the magnitude and direction of the electric field at P, which is
located at a perpendicular distance a from one end of the rod, as shown.
dq = xd,
total charge, q
7
You may find the following integrals to be useful:
@
15. Point charges +ql and -92 are placed on diagonally opposite corners of a rectangle
of sides dl and dz. Point A is the unoccupied corner a distance dl from the positive
charge, and point B is the other unoccupied corner.
(a) Determine the'potential difference Vg - VA.
(b) What is the electric potential energy of this system of two charges? Find the ratio
of ql/qz such that if a third charge q3 is placed at A, the potential energy of the
system would not change.
(c) How much work is done in moving a test charge qo from A to B?
j
/Ii
'!I
!I
I//
I
(9
)I;?;-
=
--
-4.2
.Vd-cb'),
I
I
@.)
I
Wwk dona
4 1 . Vkrb-2,
ak9rl
-k2.t1
tZ.
. '
,I
=
"t (-$,)
in Wouir\
3
10
'
& A h 6
is
16. To probe the unknown charge of a nucleus, an alpha-particle of charge q = +2e, where
e is the fundamental charge, and mass, m,, is launched directly toward it from far
away with speed, v . The alpha-particle reaches a point of closest approach before
turning around. Assume the unknown nucleus remains stationary in this process. If
the measured distance of closest approach of the alpha particle to the nucleus is d,
determine the charge of nucleus, Q = +Ze, where Z is an integer. Express your
answer in terms the electrostatic constant, k, fundamental charge, e, and the given
quantities, ma and v .
-