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A STUDY OF MAGNETIC FIELDS
Introduction
A compass is a magnet. Placed in aregion of space where there is amagnetic eld the compass will alignwith the external eld lines.Specically, the compass will betangent to the eld lines at that pointin space in which it is placed. Withthis in mind a compass can be used to“map out” the eld lines that exists insome region of space by noting thedirection of the compass needle amany points. ur!es drawn such thatthe compass directions are tangent tothem form, magnetic eld lines. hisis analogous to the electric eld wherea test charge can be used todetermine electric eld lines.An example of mapping out magneticeld lines is the placement of ironlings around a magnet. #ach of theiron lings acts li$e a small magnetand, %ust li$e a magnet, line up withthe magnetic eld. hat is, each lingis tangent to the magnetic eld at thatpoint in space. he lings are thusli$e little compasses. &n the case of the iron lings there are so many of them that one can easily see theshape of the eld lines. &n themapping you will do you will ha!e onlyone compass 'rather than manylings( placed at many di)erent pointson the table. *ou will ha!e to deducethe pattern of eld lines by placing thecompass at many places and on aseparate piece of paper drawing thecompass directions at all thelocations. &n this lab you will map out the eldlines in a region of space that is
theentire region
of your tabletop. hemagnetic eld that exists on thetabletop is due to the eld produce by
all
magnets in the uni!erse. +ostmagnets are far enough away or arewea$ enough that they will contributelittle to this eld. wo elds that willha!e a signicant e)ect are the#arths magnetic eld and the eldproduced by a bar magnet that will besupplied. he magnetic elds youobtain from your compass readingswill thus be the
net magnetic feld
due to all magnetic elds. &t is mostli$ely that these two magnetic eldswill dominate, but
e a!are
thatthere may be elds other than thesethat could e)ect your results. *oumust determine if this is the case.
rocedure
lear your lab table of
all
items beforeproceeding in order to help eliminateitems that may e)ect your compassmeasurements.When ta$ing compass readings youmay need to gently tap the compassas friction may cause it to stic$ insome positions.-se one sheet of graph paper torepresent the entire area of thetabletop.
E#ce$t !here noted% ta&ereading' o(er the entire area o) the tale to$*
&.
Ma$$ing the magnetic feld o) the em$t+ tale*
a(-se a compass to map out themagnetic led lines o!er theentire table. Present your resultson graph paper.b( State what e)ect you expect the#arths magnetic eld to ha!e onyour eld lines. c( /ote and describe any de!iationsfrom what you expect from the#arths magnetic eld.
&&.
Ma$$ing a magnetic feldaround a ar magnet
.-se two sheets of graph paper. -seone to represent the entire area of thetabletop. -se the other to representan area 01x01 cm
2
centered on thebar magnet. he idea of the secondplot is to ha!e an expanded !iew of the region around the magnet so itsmagnetic eld can be drawn moreprecisely that with the rst plot. a( Place a bar magnet at the centerof your table and use a compassto map out the magnetic ledlines o!er the entire table. b( 3eferring to your plots describeyour results. 4e sure to discussthe e)ect of the #arthsmagnetic eld, the eld due tothe bar magnet and any otherfeatures seen.&&&.
Ma$$ing a magnetic feldaround t!o ar magnet' !itho$$o'ite $ole' neare't*
a(Place a two bar magnets at thecenter of your table in a linesuch that the north end of one isclosest to the south end of theother and 21 cm away. -se acompass to map out themagnetic led lines o!er theentire table. S5555/ S5555/b(3eferring to your plots describeyour results. 4e sure to discussthe e)ect of the #arthsmagnetic eld, the eld due tothe bar magnet and any otherfeatures seen.&6.
Ma$$ing a magnetic feldaround t!o ar magnet' !ith li&e$ole' neare't*
a(Place a two bar magnets at thecenter of your table in a linesuch that the north end of one isclosest to the south end of theother and 21 cm away. -se acompass to map out themagnetic led lines o!er theentire table. S5555/ /5555Sb(3eferring to your plots describeyour results. 4e sure to discussthe e)ect of the #arthsmagnetic eld, the eld due tothe bar magnet and any otherfeatures seen.6.
Setting u$
a magnetic feldaround com$a''
.7.3emo!e all magnets from thetable. 2.Place a compass at the centerof a cleared table, nd thedirection of the magnet eld,
,
e
, and align the 8ero degreemar$ with the compass needle.'/ote9 he magnetic eldshould be mostly due to the#arths magnetic eld, but it ispossible that other eld maycontribute noticeably.(:.Place a bar magnet,
,
7
, next tothe compass with
,
7
⊥
,
e
.
;.With the
,
7
orientationunchanged mo!e
,
7
away fromthe compass until the compassneedle is 21 degrees fromnorth. +easure the distance,x7, from the compass to themidpoint of
,
7
. 6&.
Mea'urement'
of eld strengthalong two axes.7.Along the pole axis9'a(At x7 rotate
,
7
such that
,
7
is parallel to
,
e
at thecompass.
'b(+aintaining its orientation,mo!e
,
2
away from thecompass and
,
7.
<ordi)erent positions record itsdistance from the compassand the absolute !alue of the angular de=ection of thecompass. >o this o!er arange of r !alues to theedge of the table.2. Along the axis
⊥
to the pole axis. 'a( ?eeping
,
7
in the sameposition, mo!e the compassto a position 21 cm from thecenter of
,
7
and on a linewith the poles of
,
7.
'b( Place
,
2
, next to thecompass oriented with thefollowing conditions met9 i( he poles of
,
2
in linewith the center of thecompass
and
ii(
,
2
⊥
,
7
at the compass.'c( +aintaining its orientation,mo!e
,
2
away from thecompass and
,
7.
<or di)erentpositions record its distancefrom the compass and theabsolute !alue of the angularde=ection of the compass.>o this o!er a range of r!alues to the edge of thetable.6&&.
Calculation'
for radialdependence of the eld strength.7. We ha!e that the compassdirection of the needle gi!esthe total eld at the location of the compass. hus if thecompass needle is at an angle
θ
from north, the total eld isthe !ector sum of
,
e
,
,
7
@
,
2
.<or this study we ha!e notchanged the direction of
,
7
sothe total eld due to
,
7
and
,
e
is a constant !ector which wellcall,
,
7e
. he total eld at thelocation of the compass istherefore the !ector sum of
,
7e
@
,
2
as is shown in gure 7.
47e4tot42
θ
<igure 7. he net magnetic elddue to the #arths magnetic eld,47 and 42. We ha!e
,B1eB2 tan
=
θ
or
θ
tan12
e B B
=
Since 47e is constant we can writethis as 425 'constant(tan
θ
2. We assume that 4 isproportional to the distanceraised to some power. '<orexample the 4 due to a straightcurrent carrying wire is9 45 '
µ
&2
π
r(.&n this example 4 is proportional tor raised to the power of B7 '4
α
r
n,
where
n5B7(. <or
our
case we want to
fnd
n for the bar magnet for the twocases 'step 7 @ 2 in section &&&(.&f we start by writing the general form9 4 5'constant(
.
r
n
,we can eCuate this to our case for thetwo elds and write9
'constant(
.
tan
θ
5'constant(
.
r
n
. he constants on either side are notthe same. <or a Cuantitati!e analysis,where we would calculate absolute!alues of the magnetic elds, wewould need to $now what theseconstants are. hey in fact are needed to $eep theunits correct in this eCuation.Dowe!er they are not needed todetermine the radial dependence of the eld. hat is, they are not neededto determine the exponent, n. Eetsrewrite this eCuation as9 tan
θ
5 ?
.
r
n
.
Dere ? contains the constants and theunits with which we are not concerned. his eCuation has the measured!ariables, C, and r and thus we candetermine n.6.
Anal+'i'
7. <or each of the two data sets,plot tan
θ
!s. r. 2. -sing the standard procedure of logarithms, turn this eCuationinto the form of y5mxFb, wherem is the slope corresponding ton in our eCuation. Plot the datain this form, log'tan
θ)
!s. log'r(and determine the slopes foreach of the two data sets.:. +a$e a Cualitati!e statementabout the expected n !alues foreach case. hat is, from youreld maps from part & you ha!esome idea as to how stronglythe eld !aries for the two datasets. *ou should be able to statein which case the eld will bewea$er with increasing rcompared to the other case.

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