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Lecture 8 : Magneto statics . Lorentz Force Law
Last Lecture : Multiple ExpansionDipole
Vmono=q¥,r Vdifyipjrmn ,p→=§%r→!invariant if Q :O
.bg#anElectrostatics Magneto statics
÷.i..tiff Iftf to;¥Etgrq;stationary currents
source charges ZI
at
-0
2f=O Experimentally '*
HuffOpposite repells same attracts
( Opposite of Coulomb 's Law)
LorehtzforcelawB→= Magnetic Eield
if EFIP present
FI=qv→'@ odnoadiootnabegtoaw Fayettepq
• - out of theboard
any X - into the board
÷E. ←¥
We consider B→ producedby currentsuuu@QIFlIsinndgdrirgFttnYifIfffIotFaetFztIronisItTisardiatotI.o
.
Attraction
GoaliFindB→f
Ex.cc/cloitronmotiidEEkI&tixY?atiItiaiYaIetot.#
gives a centripetal forceE=qvB=m¥2=kpy= > p=qB@ cyclotron for malq
- Can be used to find p→ for a particle in an accelerator
4,13 ,R→p- Note that B→ doesn't strange speed
,just redirects
. if TH B,
let a F. + ifaParallel to B→
F=qexF=qvI×B⇒ Fca, )=O
= > §vT,Helical motion
Workdwp=Ff . DI dtavsdt
But F. tie ⇒ dWp=O
MagneticForcesdonoWor#)Again , Bfields change direction but not speed
⇒
W=sT=0
{ Kinetic
energySeems wrong ;will explain later
Cu=ents
I=daott=sa til*
I= how much charge passesthrough per time
I unit
= amperesIA =
1 Cls
I= dfgn.xddt.lvAssume da¥=OCharges move
,but X doesn't
Vectorize : I→=yu→ change overtime
since
.
e- 's move,
I4TH
ForceonawireF= fdF=fdqTxB→=fdLXG→xBkfdLCI→xB→)
since Elldl, F=fICdfxB→ )
Typically,It constant along wire
→
ftp.I/de@#rayFeFF
for vca speed oflight
Ex.
Force on loop
÷For wire currents ,net charge =0
-
9llowsFpto_domnate.yyfB@Itoba1ance.m
?
#Fp ? up ⇒I ? clockwise
€F. =IL→xB→= IDB
, up
Fp =Fa= mg⇒ Iihf
increase current =) FB > For mass
goesup
Looks like work is happening?
It is , but not by B→
The battery increasing the current is doing the work
Mifflinextra FI dpg¥ofE
t u
battery Pushes e-'
s to opposeFT=XquBWbattery=f(Xau B) ( wdt ) I=Xwheat
=IaBh=FBh
!
ftp.onITQ.nportiTSurface & Volume Current Density have intrinsicspin apart- from motion
.
Magnets are due to
/I#% Edit
.se#naWaeYidIMm.*e
~ E=Fe+dd÷i=£a
.it#Asi=6ddlyv=oT=KDF=fdqTxB=fdA6CexB)B=fdA(kxB
)
## dat F=dd¥+= volduemnesigayrrent
=pF=FD ftp.fd~CFXB)
I=fFda+=fsFdAudqdt
F exiting a closed surface
§sF.de = ddottoht '= ÷ daftcin )
iv. Foh '
"
fdofedx⇒
T.FI#=0( continuity equation )
In electrostatics, #ftp.hy.ge nation
dt
Ex.fi#gwred) I uniformly distributed
0µAJ=AI=f€b) Suppose J=Ks
I=fJda+= folks)atsds )=2tKfo9s2ds=2gIK@
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