\~.
-46. Parallel conducting tracks, separated by 2.0 em, run north
and south. There is a unifonn magnetic field of 1.2 T
pointing upward (out of the page). A O.04O-kg cylindrical
metal rod is placed across the tracks and a battery is con­
nected between the
tracks, with its positive
• • • • •i
terminal connected to
the east track. If the
s
• • • • •
current through the rod
• • • • •
is 3.0 A, find the mag­
Cylindrical--=~~~
metal rod
•••••
nitude and direction of
the magnetic force on
+
the rod.
·....
'F5::: l (LxE )
;::. "l
--
" " '=
l"g~) f') ~
:::. ~ .OA)
~
-
..
..
_.~
N ~I' -\-"'" \
F .. r~ ~s. ~ ~ to
...l.. ~
\ t-B =.
t)
O. O~ 0 Iz.
:I':..."3.,<JA
«}.. ,0,-_-._ """'J(\.',1') s\"\ G\Oi)
_. __ ._.-. - _..
8 16--1,2T
~ C) ., ~ N
Gl)
48. A straight, stiff wire
oflength 1.00 m and T= 0
T=O
•
•
mass 25 g is sus­
• • •
pended in a magnetic
•
field B =0.75 T. The
wire is connected to
••
1.00 m· • •
an emf. How much
••
••• B
current must flow in the wire and in what direction so
that the wire is suspended and the tension in the sup­
porting wires is zero?
d­
1= 1.0 A
49. A 20.0 cm x 30.0 cm·
rectangular loop of wire
carries 1.0 A of current
e~quct ~r ~.C4~
clockwise around the
c;SProblems 49, 50, and 107
loop. (a) Find the magnetic force on each side
-,­
of the loop if the magnetic field is 2.5 T out of the pag~e_-------l--~-...,~"""'------\
(b) What is the net magnetic force on the loop?
O+ocm YL
-30.0cmx
+L...
V C9
o cb 00
.~
-:::.
~.
5
;t
G0BO
-7
l
t= l
~ LOA
(3J
':71­
""'1.. U;S "~
:
=
e.S 1") (0, ZO'i"'') (\,04)
': O. S N
~--- SC)
I)f.~)~ I r?-F' <uJ
FI I
-;;. 0 S' f'J
I
It:7.-I-=- ) F~ )
"'t.,..~ ~(U-..
0'"
F\
\5
Si"u.
o.n..~ F~
--tk. \ 'i) ¥ \' ~
ll-~,J...
'\.) tL"t"J.
(M,
b­
o-.~
c""" ------~~
s~d-t
lOOt
i
50. Repeat Problem 49 if the magnetic field is 2.5 T to the
left (in the -x-direction).
--
c--_·
Fl.-
-:.
F"i
~-O
s,,...Q
9
= VI \~
5)" () ~O
t~3 \~ ) t=, \ :: I
t\ fD)V\ts
c>
L'\3
vt
c)
=. ~c) A.)(Or Z tn) (2. Sl) ­
+: -\~ r~y-
f 3
f~~"y;. ~ ... \-u --\k
t:"fl-tA- e 0
o.stJ
pt-~
S \"" c:...
55. A square loop of wire of side 3.0 cm carries 3.0A of
current. A uniform magnetic field of magnitude 0.67 T
makes an angle of 37° with the plane of the loop.
(a) What is the magnitude of the torque on the loop?
(b) What is the net magnetic force on the loop?
'q)
Ac:..~::.
N~
N 1 ~ '& 5 ~V'\ e­
S~e-
i
CO~\
~(.,.....,
QVI.
~J
I
<J.,.
1
13
1::; 3.oA
'g -=- UJ~1--1
It : .- ~I ()~ 'Vt'\)( O,D ~~) ::: ~ 'lllULtM~
(t -= a-'" ~ b"\w.."" i!> "",cl Ik" L f t "J.,
~ qc ' '3100~ 6~o
'\: -= ~.OA-)(q X\o-LlYT\'1..)lt),(:)'}I) s\'" $1°
~ \.. L.\ y X10- ~ 1'1. ""
~ -/'. ~ J-.. b.p
)
b) ~¢=o
~vo
Q",
ON
Jl.J..t ,0,
e-~.. o"o.)..J:....
~~o~.
lq.
:61. Two wires each carry 10.0 A of current (in opposite
directions) and are 3.0 rom apart. Calculate the mag­
netic field 25 cm away at point P, in the plane of the
wires.
AA P~'II\\-"P I ~\
~ p~ ~cl "Et,....ir
1
----~-- 3.0mm
I
I
lJ ~A'\-o
0,"-,-
25 em
c)f-- ~~ f ~J
S\\"CL ~Sc........ ~ "J~.-
lp
~w,lI
e.J~r~
c."'VlCA1
21\r
21\~'2.Si1
~
I
= '7. 9 t
1
fA)
'&1. =- 4"'tiX Icr~ \u.oA
-x \ o~1
k
-:------­
bt.- ~ ~" I~ -b l'
'l,..-"It
(p. 1.-s1n)
.
~.::.. '8>).. 7") ~
71. Two long straight parallel wires separated by H.U cm
carry currents of equal magnitude but heading in oppo­
site directions. The wires are shown perpendicular to
the plane of this page. Point P is 2.0 cm from wire 1,
and the magnetic field at point P is 1.0 X 10-2 T directed .
in the -y-direction. Calculate the current in wire 1 and
its direction.
(CO
l-r,\ :~. . I ''"vI<
~
\
.\'~"+' 6'~
f!
PQ'f\,~
,~~
"bJ"i "\. ."J1-
. '
~ "~"'" Ie> "~O~ ~
S~
l.:
\\....\'\l
<>-'i'\e}..
4~
~~I~
~
!!o
~,\\ ~Q
~~ ­
z.n(z..,..
~1\ 0~ \~"Z.T)
If "T' ~
I 0 - J- r~
)f­
\~IO-2
\.
c.!I'
C-<'v.J
..1,\..0. ;.., ....j .£w~.",
~v..o~ \o.c... o~o~.Ie,~
f'1o:l,'~~
clo~'"
M-t:>
\
\
l67. Two long straight wires carry the same amount of cur­
rent in the directions indicated. The wires cross each
other in the plane of the
A
C
paper. Rank points A, B,
-d~.-d~.
r
e, and D in order of
decreasing field strength.
I
d
~!
Cw...t
~orl~'" \.J.. ~rt
d
-d~l-d~.
B
D
1
I
'B \ i >
Ij,
#-­
i h:, ~ "~t ~
V\
A ~~
"9;>,
.:I
T
t...
o~ Q~ ~ P"''f-''';
1> 0.;..- D
~
~
,',:»
()~ ~ 1. -kk ~o-,. oJr.. A I ~~ <. O'I.J b '-'
1$ ":. ~ \ ~ R1.
= _~
'Uta
- ~'1. + ~Q 1
Z. ~ c:l..
:: J!..u ~ "\" Jb-'1l,.. 'i\
l.. 1\ cl
b
C
1+
M ro"
Il"~
•
:-
?~ .J­
2 'i'i d
=
~ "L _
'11\ cA
"z..:rr cA
,l
~ ::~""l.
t 1f 'lGl
4-
~
'z:~r '1 J-
~.>., ~ "''Ii
1'1
J; '"
It.
H~J- t':A\,
9 Oh~ 1:> ~ I~\I~ !A,rp ~
~o ~ At "'"-6. C~ \ '" "-k
~ h·J.-~
\
\5 VJ~
W \ ( ll..o
6J\..
G\(~'''''
1 S\...Q~ ~ ~ $JcroV\~\.
o
Sl" C"A.',
\j ~Lo~ N ~~t~ "",,il'~
S'f.,.Q~), 'oL ~~~
~
~ i~ f)YJ'" ;j)~'a 'kr~ ~\~u.. ~
C-foVt\c:.J
4-~,,",
~o ~ ~~ 'o,,'~ ~
A.
99. Two conducting wires perpendicular
Wire
to the page are shown in cross section
as gray dots in the figure. They each 10.0 1O.0m
_ _op
carry 10.0 A out of the page. What is
10.0
the magnetic field at point P?
13 i'~ -t6~~~
MA h",,- s-o
13..1.. +0 (~~......,
mI
m!
•
• Wire
"\
'I \
~ )$ z-' ~ jJ.~ -r
Z:n,
\ G,)
\
~
/
/
r::: ~ ~O'" )1..~a_ )-z.
=
\L1.\\¥'\
13,\~
t X)C-1-~~
ll
\/
A)
\\\1.\~)
"(....l\
= \. 41. )( N- T- T ":: \~)
'B,,c.:. 13, Co~ e
B\ y -:: ~ I ..s I >'\ ~
~"l.X -=
"'2
-
D2. '1 ~.\-
\'",,)0
\
~ \~
-= \\'-t'-~I~T-\ (.~"tS"'~ "\~ll;)"':t-..,:: \-l )( \~- '"T
-1-\
-~ -
\
)( cO"'"'.fuV).t ....~
C-C41•.,c.al
~ G(:)~f\)1f\ e...h oJ..~
~o .1
A_.,W
{)o.b-JeJ ....t-o
C1-) w"".i-~
D'
44
&0~
\
e "'j ~\.. L
~~"
k'- r 'j~~ Goo\.- (I<>.
~ 'W/_\.. .... ~IQc\.I ... ~.GJ"""'"
VI"E, L-,
d.OIU
f't)
tw) 't-.~~ J..,.c1­
~l....... ? lc) w~;)
-.... J.12?
(..W(...
""~
-\1-. d.,. c.h'i>o" o\- ~ Wooa.)...Jat. toru. c ...
~/08-? (d.) ~~'u ~\.... ~p""h....L..
oL~.~o.~-.h-c.. ~ru.
v. ~.l-~ol tz.
a.j bL-c~
a-
mo oJ ,
'''' lu..u.-6-
)<
?
K
~
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'*.'" ~U"~ *
.-tix rc ~ ;)
wt..
I
'Eo M.
\""UIIC-.
v~~
CLI"'\
(==
Fe; .
1F~
(i) f
Ft!>~,..
~
~ 6~
(JV\
e
cppQ.)\t (2)
Lwrt.~\-\~
F'3 =
J)
"'!
J: L~~~
(~~~
~~\V
e :qO
=!
=
It). \~
\. ?» lin
)C
ftM.f;>;'~~ ~~ ~~
Q,OJ ~\....,) ~~
\.0....... 1. t.-t l...
c.;J.~ ~ ...
Go. . . - . .
fA.
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"'7 \,.l,.........l.
\-w<..e-.l'\ ~
-\-0
~ ()"
o
~~~~--~
~ c.a ?
~~~
e :2S
B
~ \~ t-\~.... ~\vo\.O-t-.Jrk... ~k..
, ""
-~
,
J"""'h....J.c... ~ e,I.i"\_'l ... ~
\. .I
J.:HC.'..lc.c..6.. c,s ~ ~low ~
ho;' 'l:'U "" ~ I &.-> \...cJ- \. ~ -\-l-.- ~r""'~
o
\...13
VBL(L13)~
~
••
0..
S IN C-c;.. C-I2..
~ -=
"'6A ~'\~ e
~': 1w -::: ~,o -- )l " os ~"
~\.3W"~
g =q 0
u
~
-b 5 ~
="2- s­
-=CQI ,-\\.hdC-J-r) (\, ~vP\1r) ~',~ L5
-:: 5", \8' ~ \0 -~ I"Y't' Z.
or ~
S I'~ X\0·"\ w~