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Fall2012
Phlzsics 22
Exarn 3
-
Chapters 26,
27 .28
Do all your work in the space provided. If the work is not shown, then credit will not be given. Express
your Emswer to three significant figures, unless indicated otherwise. Please underline or draw a box
around your final answer, and include the correct units with your answers.
L. a.
Write Kirchoff's loop equations for each of the
simple loops. Take the loop currents to be h, lz
-"8
and Is, as shown. Sirhplify the equations by
combining like terms. Do not solve. (9)
. +-Vol\ *Vgf__*
z+,
I3 -- O
th
tt
I
40e)
*70I,* \ool-,-'frTl=-O
Is
-40
I t';tTu+\5"\=too
100
v
7
b.
Write the equation that allows you to find Ves. Do not solve. (4)
Ve*
- -1oIr +"o3 u
T
t3
2.
A simple circuit is shown to the right.
a.
If an ideal ammeter is inserted at point B, then what will its
reading be? (3)
^
tDo t- srrL +- 7Dl
I
roo
=ta
\>- o =
D. g-))
A
7
b.
If an ideal voltmeter is connected between points A and B, then what will its reading be? (3)
V+a
= il2 L =- toQrbv)
+t ;1l*
= :=:-\
1
A galvanometer is used in a real ammeter and a real voltmeter. The resistance of the galvanometer
is 10 ohms. In the ammeter, the shunt resistor is 1.2 ohms and in the voltmeter the series resistor is
820 ohms.
c.
What is the reading on the real ammeter when inserted at point B? (No voltmeter connected.)
a*^-r.*e-b,e-^
-l7D t
[=f,orL
Io' --
L_1
d.
L
1)-(,DJ
\1'o1 5L
IL
5e
*r-
!
l.oJ
la-ti
=- lDo
/\
5
reading on the real voltmeter when connected between points
ammeter connected.) (5)
\Atrhat is the
$7o
Rv 1- t0+?7/o:
-.ct,-)
v, \f*<)w
A andB? (No
rt-'-s I st-a'^-
\ , 'oLt)D) : +l,lL SL
r-*\--l
/
r-t
tz
P2
Ttto
'ot*ru
-+io
-}"
*r'-:\
^\0o {- ''t1.lL i
t\
L3
V*r=
c-c-
I -"1D I- --o
T -- b. klt
10','
.17,-'n-
|
Lt-i
10?
f :
c-*
-r1o};O
$.ssl At
'lu
S
tb
An
switch is located between points A and B in
the circuit.
a.
SI?ST
Find the potential difference Vee. (6)
.-lL +-loo f -rl f
?ot2
f '-o
aot)'\ =' ,
T = D.DlblA
Vo,
=
Too{g)-1+l *voo[.ottr)
=- -L Jr V,)1
V*
=-
*-1,?t*
"-==#-F
The switch is now closed. Find the magnitude and direction of the current flowing through the
switch.
(8)
TooT\ - 74u I-_
_ooll rs\fl, I )f
\Voo
=
=
l
:-\
\.;"
-)^
t ?oO -)z{o
\
--o 5bo
looo
+ lboo
\5-oo oo
- +ado
\
+DD
*--
Il
F
Dopo
ArV9
?
tr
switch
4.
switch 2
1
In the circuit showrL at time f = 0, switch 1 is closed.
a.
Find the voltage across the capacitor at t = 1.2 msec '1
a-fter switch 1 is closed. (6)
Ltr -
v,=
;
v""-)
|
a loo l\-u
1
V,
[Du (
a
\DD
(t
100
YY<i'1
volts
- ulrt.o
1
o*)=
0,&f(oL
zo(+X
T=
+r E^--- ,-'-5]z'-&-
- ['rr
)
t -. r-l)
2- ll, b (r-
#
p
At this time (t = 1,.2msec), switch 1 is opened and switch 2 is closed (done simultaneously).
Find the magnitude and direction of the current flowing through the 200 ohm resistor 2.0 msec
later. (6)
Vr:VrL
-?-
=Vr,,rtVr*
"WoL t-t'l) f
=
vv/'
- V,
-f)-- =
:2.U
1bu
'
11. t
'l oo
-W
= 0_1[
RL ,
_,
Li':'
10r-,
(t nr" )
-- -L,? f
lo
-3
-1'
-'2^?vto
n
- otrT
U
=- 0- llr\
Iurto)
;
*,\
)r, rL
lv
An electron (q = -t, m"= 9.1L x
10-31
kg) has an initial
,L
velocity of ao= 4.0 x 105/ m/s (see diagram). A
uniform electric field,
E = -2000
uniform magnetic field
E=
iN/
C' and a
i',
3'0110{
ur"present.
If you were to look at the motion of the electron
from along the r-axis, which type of motion
would you observe (1. or 2)? (2)
b.
\zVhat is the value of the radius of the circle
whicht:"**Tf"'n'
r--.:;a
in
=ffi n.i"
o,
l
\
(* l,
fl
+
I
c.
How far along the x-axis will the electron travel when it undergoes one complete revolution?
rt'r,lt
= V,fl Xlo
?( =
v-t
urLt-
.
zn-[z-
1r
)
=
X=
o -v\A,t\Xlo 'n)(''\
* L,+i
t,ttr rlo
DD]
+ rt" t
"1
?
fi)
qe.u
''xl" )
"^^-
il
A long, straight wire carries a current Il. A
rectangular loop carries a current 1z in a clockwise
directiorL and the loop is in the same plane as the wire.
a.
&h
\
l+,-
f
)rY
Find the magnitude and direction of the force on
loop segment 1-2 due to the magnetic field of the
Iong wire. (4)
I,= f ,.;8, ,i1o' = IrrL I Et
=
_____>
rl
[ -o [D'i-\t,
\
F r-b.
Y
Find the magnitude and direction of the force on loop segment 4-L due to the long wire. (6)
Lr--r
d{- h
F=
i1,t" --r.,-L\t D1
" \ >TY)
D,-.'
W-l%
-t l3
JD
r*r(=
M,
), L- A
G-hT
*>
D+V'2
/l t*
\
v
c.
Find the magnitude and direction of the torque acting on loop due to the long wire. (Careful!)
(3)
+- )n'r t"l --f* '. Lo'a-\ "")
T'- O
F
1F
a
t]
7.
A circular loop of wire with a radius R, and carrying a
current I lies in the y-z plane.
a.
Start with the Law of Biot-Savart and derive an
expression for the magnetic field on the r-axis at a
distance r from the center of the loop. (6)
B?
=- 1), =-O
J9^=J3e*(9-=H Ll.-tLlt
rl-"
-2
Y-t
R
-1?n
i rlP
vtrY
Dr=
DF=
I,,U
-
:.. 1^z
> L*'vt)
\
t-
Prt"b
!"
b.
The diagram below shows the loop in cross-section. Draw small compasses at each of the five
(5) dotted positions showing the orientation of the compass and label the north-seeking end oI
the compass. (5)
y
\
rl
v
8.
The diagram shows the end view of two long
wires whose lengths are parallel to the z-axis.
They carry currents I in opposite directions, and
are placed a distance D to the left and right of the
\";
\(
--\-
h,-
v&\
origin.
a.
,
Find the magnitude and direction of the
magnetic field at point P, a distance y above
the origin on the vertical axis. (6)
E= - \)Lr;0-* Ro)*$
D
D
f ur'
tA:=:\g-
i.Hfu-) ry--
uLrTrvT)W,wcI->
RT
r o"r)
\
f
Y
A third wire, carrying a current l out of the page, is positioned parallel to the first two wires
- passing through point P. Find the magnitude and direction of the force on a length L of the
and
third wire. (4)
e
t---
tr : !-LBe o*7oo
Irz
.tr{-
,
.l
rr- [u*+3
)
l')
+_, sirl",4
--
lD