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OverviewElectrostaticsElectric PotentialDielectrics and CapacitanceElectric CurrentDC CircuitsMagnetism

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ElectrostaticsCharge is carried by subatomic particles

protons, electrons!

" 99# o$ all charged e$$ects caused by electrontrans$er

Charging by Conduction

" Physical contactCharging by %nduction" &o physical contact

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Coulomb’s Law'his la( determines the $orce o$ attraction orrepulsion bet(een 2 charged ob)ects

" ε 0 is a constant * permitti+ity o$ $ree space

" Positi+e $orce repulsi+e, negati+e $orce attracti+e

" -emember. $orce is a +ector

F Q Qr

q = 14 0

1 22π ε

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Electric field lines +isualrepresentation o$

an electric $ield1" More lines

stringer $orce

" Point a(ay $rompositi+e, to(ardnegati+e1

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Electric Fields and conductors'he electric $ield inside any conductor is

ero

'he electric $ield is al(ays perpendicularto the sur$ace o$ a conductor

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auss’ LawElectric 3lu . 'he amount o$ an electric $ieldpassing through an area

5auss6 7a(. 'he total electric $lu passingthrough a closed sur$ace is proportional to thecharged enclosed in that sur$ace1

Φ = Qe n c l o s e d

ε 0

Φ = E A c o s θ

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Electric Potential Ener!yElectric Potential energy can be determinedusing mechanics

Electric potential is de$ined as the electricpotential energy per unit charge

∆ U q E d = −

V U q

W q

= = − ∆ ∆U q V = −

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E"ui#otential lines or surfaces n e uipotential sur$ace is a sur$aceo+er (hich all points ha+e the same

potential1" n e uipotential sur$ace must be

perpendicular to the electric $ield

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Potential due to a #oint char!e

V Qr =

1

4 0π ε

" -emember. potential is a scalar

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Ca#acitance capacitor is a de+ice that stores electriccharge1

'he capacitance o$ an ob)ect is de$ined as.

Capacitance is measured in $arads1

C QV

=

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Parallel #late ca#acitors and

dielectrics3or a parallel plate capacitor t(o conductingplates (ith a +acuum bet(een the plates!

$ten, an insulator :no(n as a dielectric isplaced bet(een the plates to enhancecapacitance" Dielectric constant. measures the strength o$ the

dielectric

C Ad = ε 0

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Ca#acitors and ener!y charged capacitor stores an amount o$electric energy gi+en by

" 'his energy can be thought o$ as stored in the electric$ield bet(een the plates1

U Q V = 12

2

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Electric CurrentElectric current is de$ined as the amounto$ charge that $lo(s past a gi+en point in

a second

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Ohm’s Lawhm6s 7a( related the resistance o$ an

ob)ect to the decrease in electric potentialacross a point and the current $lo(ingthrough that point1

RV

I =

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Electric ResistanceElectric resistance is the innate ability o$ amaterial to inhibit the passage o$ electrons1

"Measured in ohms1

" 5i+en by the resisti+ity as (ell as the geometry o$ theob)ect1

R

L

A=

ρ

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Circuits $ emf and terminalvolta!e

de+ice that trans$orms one type o$ energyinto electrical energy is a ;source o$electromoti+e $orce<" em$. the potential di$$erence bet(een the terminals o$ a

battery (hen there is no current $lo(ing to an e ternalsource1

" battery has some internal resistance

" 'he real +oltage o$ a battery is then

V E I r = −

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Resistors in series

=oltage andresistance areadditi+eCurrent is constante+ery(here in aseries circuit

R Re q ii= ∑

V V t o t a l ii

= ∑

I I I t o t a l = = =1 2 . . .

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Resistors in #arallel

Current additi+e=oltage is constant

e+ery(here in aseries circuitMore resistors smaller e ui+alent

resistance1 1

R Re q ii= ∑ I I t o t a l i

i= ∑

V V V t o t a l = = =1 2 . . .

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Com#le% Circuits

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&irchhoff’s rules

>unction rule. t any )unction point, thetotal current into the )unction has to be

e ual to the total current out o$ the )unction17oop rule. 'he sum o$ changes in

potential around and closed loop is ero1

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&irchhoff’s Rules

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'a!netism

E+ery magnet has t(o poles. north andsouth

Magnetic $ield ? magnetic $ield lines.analogous to electric $ield" Direction. points north to south

Electric current mo+ing charge!produces a magnetic $ield

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Force due to ma!netic fields

'he $orce on a charged particle mo+ing througha magnetic $ield

'he $orce in a current carrying (ire immersedin a magnetic $ield

F q v B= s i n θ

F I L B= s i n θ

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Ri!ht hand rule

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Am#ere’s Law

mo+ing charge current! creates a magnetic$ield1

" 3or a long (ire, ∆ l 2 π r

" '(o (ires can attract or repel due to this e$$ect1

" solenoid is a long coil o$ (ire1

B l I ii

e n c l o s e d ∆∑ = µ 0

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Faraday’s Law

changing magnetic $ield induced an em$1

" current produced by an induced em$ mo+es in adirection such that its magnetic $ield opposes the

original change in $lu 7en 6s 7a(!" coil rotating in a magnetic $ield is a good e ampleo$ this1

E N t

= − ∆ Φ

∆