Physics Notes Electromagnetism Davesim

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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