physics notes electromagnetism davesim
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8/6/2019 Physics Notes Electromagnetism Davesim
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Electricity ElectromagnetismInGravitation,we learnt that amass (A) gives rise to a gravitational field
around it. Another mass (B) in this field will experienced an attractive
gravitational forcebymass (A). InElectricField,we learnt thatacharge (A)
gives rise to an electric field. Another charge (B) in this field will either
experience an attractive or repulsive force by charge (A). In
ELECTROMAGNETISM, we will learnt that a moving charge constitute to
current. Besides electric field, the current gives rise to a magnetic field
around it.Wewillalsodiscusshowamagnetic forcecanbecreated in the
presenceofcurrentandmagneticfield.
Dave Sim @
Raffles Institution
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IN TRODUCTIO N
MAGNETICFIELD
The number of lines per unit crosssectional area is
proportionalto themagnitudeofB. Ifthe field isuniform, the
fieldlinesareevenlyspaced.
Werepresentthemagnitudeanddirectionofamagneticfield
by themagnetic flux density B. (analogous to electric field
strength,E inelectricfieldandgravitationalfieldstrength,g in
gravitationalfield.)
ItsunitistheTesla(T).
s in
s in
=
=
B
B
F B I LF
BIL
Amagnetic field is defined as the region in space in
whichamagnetwillexperienceamagnetic forcewhen
placedatthatpoint.
The direction of themagnetic field is the direction in
whicha smallmagneticnorthpolewillmove ifplaced
there.
ThemagneticfluxdensityBatapointinamagneticfield
is the forceperunit length thatactsonawirecarrying
unitcurrent,lyingatrightanglestothemagneticfield.
N
S
(a)Barmagnet (b) Ushapedmagnet
Fieldlines
closetogether
Blarge
Direction
ofBatP
B
small
Parallelfield
linesBisconstant,i.e.a
uniformfield
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C O NC EPT 1 - M A G NETIC FIELD DUE TO C URRENT- C A RRYING C O NDUC TO R
CASE1 MAGNETIC FLUX DENSITYDUE TOAN INFINITELYLONG STRAIGHT WIRE
CASE2 MAGNETIC FLUX DENSITYDUE SOLENOID
Aconductorcarryinganelectriccurrentalsosetsupamagnetic
field.
where B=fluxdenstiy
I=currentinthewire
r=perpendiculardistanceofPfromwire
0 = a constant of proportionality known as the
permeabilityoffreespace( 7 14 10 Hm ).
Current flowing through a solenoid (L >> d) also sets up a
magneticfield.
n=numberofturnsperunitlengthof solenoid,N/L
ateitherendofthesolenoid,B=(nI)
2
= o
IB
r
I
r
P
0= B n I
currentflowingintopaper
currentflowingoutofpaper
current flowing
out of paper
Fig. 10
current flowing
into paper
B
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CASE3 MAGNETICFLUX DENSITYDUECIRCULARCOIL
Current flowing through a circular coil (L
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CONC EPT 2 - M A G NETIC FO RC E O N A C URRENT- C A RRYING CO NDUCTO R IN A M A G NETIC FIELD
ACURRENTCARRYINGCONDUCTOR INAMAGNETIC FIELDEXPERIENCESAFORCE.
DIRECTION OFMAGNETICFORCE
MAGNITUDE OF MAGNETIC FORCE Themagnitudeof the forceFonawire inamagnetic field is
directlyproportionalto
1) thecurrentIinthewire
2) thelengthLofthewireinthefield
3) themagneticfluxdensity,B
4) theanglebetweenthecurrentand themagnetic flux
density,B,whenbothareinthesamedirection.
1) Magneticforceismaxwhen is =902) Righthandgrip pleasenotethatforceisIXB,whereI
andBareinthesamedirection.
( ) ( )sinmagnetic
F L IXB B I L = =
sin=B
F BIL
I
B
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A PPLIC A TIO NS OF CO NC EPTS
CASE1: FORCESBETWEEN TWOPARALLELCURRENTCARRYINGCONDUCTORS
Case1:LikeCurrentattracts Case2:Unlike Current repels
Note:MagnitudeofFB
Theampereisthatsteadycurrentwhich,whenitisflowingineachoftwoinfinitelylong,straight,parallelconductorswhichhave
negligibleareasofcrosssectionandare1metreapartinavacuum,causeseachconductortoexertaforceof2107Noneach
metreofthewire.
X Y
I1 I2
r
X Y
I1 I2
r
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B
Three longverticalwirespass through the cornersofan
equilateraltrianglePQR.PandRcarriescurrentdirected
into theplaneof thepaperandwireQcarriesacurrent
directed out of the paper. All three currents have the
samemagnitude.Whicharrowshowsthedirectionofthe
resultantforceactingonP?
B=oI/2r.6.0104T6.7105T3.2103Ntowardsthe
wire.
ThefigureontherightshowsalongwireXYcarryinga
currentof 30A. The rectangular loopABCD carries a
currentof20A.Given:a=1.0cm,b=8.0cmandL=30cm.
(a) Calculate themagnetic fielddue to the current
inXYalong
(i) AD
(ii) BC
(b) Calculatetheresultantforceactingontheloop.
B
Three long wires W1, W2 and W3 carrying the same
current I are arranged in the configuration as shown
below.What isthedirectionoftheresultantforceacting
onW1?
A Totheright
B Totheleft
C Downwards
D Upwards
P
RQ
A
B
C
D
E
I
a
aa
W3
W2W1
D
C
20A30A
Y
X A B
L
a b
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CASE2: TORQUEON ACURRENTCARRYINGCOIL IN A MAGNETICFIELD
MagnitudeofFB
Case1: =0 i.e.whentheplaneofthecoilisparalleltoB. Case2: =90,i.e.whentheplaneofthecoilisperpendicular
toB
I
P
S
Q
I
R
Y
B
(a) SIDEVIEW
current
out
b
(b) TOP
B
P
current
down
Q
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CONC EPT 3 MAGNETIC FORCE ON A CHARGED PARTICLE IN A MAGNETIC FIELD
MAGNITUDEOF MAGNETICFORCE
Considerachargedparticlemovinginauniformmagneticfield
withvelocityv.
Note:
1) Note the sign of the charge when determining the
directionofFB
2) Thepath travelled isa circularpathas themagnetic
forcewhichisalwaysperpendiculartothedirectionof
motionprovidesthecentripetalacceleration.
Case1:PostiveCharge
Case2:NegativeCharge
72.8 10 Hz
Anelectronofchargeeandmassmdescribesacircularpathofradiusrwhenitisprojectedwithvelocityvinto
auniformmagneticfieldoffluxdensityB. Showthatthefrequencyofrevolutionisgivenby2
=Be
fm.
Howmanyorbitspersecondaremadebyanelectronifthefluxdensityis1.0103T?
(e=1.61019C;m=9.110
31kg.)
sinB
F Bqv =
Fm=BQv
v
v
M
FB
v
N
FB
sin
sin
sin
B
B
B
F BIL
dqF B L
dt
F Bqv
=
=
=
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2.6107ms
1
1.1107s
2.21012J
7.0
10
6V
An particle, ofmass 6.7 1027 kg and charge +2e ,was injected at right angles into a uniform
magneticfieldoffluxdensityB=1.2T.Ittravelsinacircularpathofradius 0.45m.Calculate
(a) itsspeed,
(b) itsperiodofrevolution,
(c) itskineticenergy,and
(d) thepotentialdifferencethroughwhichitwouldhavetobeacceleratedtoachievethisenergy.
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Undeflected
Undeflected
Upwards
undeflected
Thefigureshowsaparticle,ofcharge+qandmassm,enteringauniformmagneticfieldBthatisdirected
downwards into theplaneof thepaper.Theparticle is travellingwithvelocityvatrightangles to the
field.
Auniformelectric field isapplied in thesame regionas themagnetic field so that theparticlepasses
throughundeflected.
(a) WithanarrowlabelledE,thedirectionoftheelectricfield.
(b) Stateandexplaintheeffect,ifany,onaparticleenteringtheregionofthefieldsiftheparticlehas
(i) chargeq,massmandspeedv,
(ii) charge+q,mass2mandspeedv,
(iii) charge+q,massmandspeed2v,
(iv) nocharge(i.e.particleisneutral),massmandspeed2v.
X X X X
X X X X
X X X X
X X X X
X X X X
particle
region of uniform
magnetic field into
planeofpaper
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