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@