# Chapter 28 Sources of Magnetic Field

Size: px
Start display at page:

Transcription

1 Chpte 8 Souces of Mgnetic Field - Mgnetic Field of Moving Chge - Mgnetic Field of Cuent Element - Mgnetic Field of Stight Cuent-Cying Conducto - Foce Between Pllel Conductos - Mgnetic Field of Cicul Cuent Loop - Ampee s Lw - Applictions of Ampee s Lw - Mgnetic Mteils

2 1. Mgnetic Field of Moving Chge - A chge cetes mgnetic field only when the chge is moving. Souce point: loction of the moving chge. Field point: point P whee we wnt to find the field. Mgnetic field fom point chge moving with constnt speed B q vsinϕ 1-7 Wb/A m N s /C N/A T m/a (pemebility of vcuum) c (1/ ε ) 1/ speed of light

3 Mgnetic field of point chge moving with constnt velocity B vecto fom souce to field point qv ˆ ˆ / Moving Chge: Mgnetic Field Lines - The mgnetic field lines e cicles centeed on the line of v nd lying in plnes pependicul to tht line. - Diection of field line: ight hnd ule fo + chge point ight thumb in diection of v. You finges cul ound the chge in diection of mgnetic field lines.

4 . Mgnetic Field of Cuent Element - The totl mgnetic field cused by sevel moving chges is the vecto sum of the fields cused by the individul chges. dq nqadl (totl moving chge in volume element dl A) Moving chges in cuent element e equivlent to dq moving with dift velocity. db (I n q v d A) dq v sinϕ n q v Adl sinϕ d d Idl sin ϕ Cuent Element: Vecto Mgnetic Field B Idl ˆ Lw of Biot nd Svt

5 Cuent Element: Mgnetic Field Lines - Field vectos (db) nd mgnetic field lines of cuent element (dl) e like those geneted by + chge dq moving in diection of v dift. - Field lines e cicles in plnes to dl nd centeed on line of dl.

6 3. Mgnetic Field of Stight Cuent-Cying Conducto Idl ˆ B 4 π dl ˆ dl 1 sinϕ dl sin( π ϕ) dl x x + y B I x dy I 3/ ( x + y ) x x + If conductos length >> x B I ) x I B π I π x ( B diection: into the plne of the figue, pependicul to x-y plne Field ne long, stight cuent-cying conducto

7 - Electic field lines dite outwd fom + line chge distibution. They begin nd end t electic chges. - Mgnetic field lines encicle the cuent tht cts s thei souce. They fom closed loops nd neve hve end points. -The totl mgnetic flux though ny closed sufce is zeo thee e no isolted mgnetic chges (o mgnetic monopoles) ny mgnetic field line tht entes closed sufce must lso emege fom tht sufce.

8 4. Foce Between Pllel Conductos - Two conductos with cuent in sme diection. Ech conducto lies in B set-up by the othe conducto. B geneted by lowe conducto t the position of uppe conducto: I B π F F L I' L B I I' π F I I' LB I' L π Two long pllel cuent-cying conductos Foce on uppe conducto is downwd. - Pllel conductos cying cuents in sme diection ttct ech othe. If I hs conty diection they epel ech othe.

9 Mgnetic Foces nd Defining the Ampee - One Ampee is the unvying cuent tht, if pesent in ech of the two pllel conductos of infinite length nd one mete pt in empty spce, cuses ech conducto to expeience foce of exctly x 1-7 N pe mete of length. 5. Mgnetic Field of Cicul Cuent Loop Idl ˆ B Idl B I dl db 4 π x + ( ) I dl db x db cosθ + ( x + ) ( ) 1/ x θ I dl db y db sin x + x ( x + ) ( ) 1/

10 - Rottionl symmety bout x xis no B component pependicul to x. Fo dl on opposite sides of loop, db x e equl in mgnitude nd in sme diection, db y hve sme mgnitude but opposite diection (cncel). B x I dl I dl I 3/ ( ) 3/ 4 ( ) 3/ 4 x + π x + π ( x + ) (π ) I B x + ( x ) 3/ (on the xis of cicul loop)

11 Mgnetic Field on the Axis of Coil NI B x + ( x ) 3/ (on the xis of N cicul loops) NI B x (t the cente, x, of N cicul loops) N I A N I ( π ) B x π + ( x ) 3/ (on the xis of ny numbe of cicul loops)

### Course Updates. Reminders: 1) Assignment #8 available. 2) Chapter 28 this week.

Couse Updtes http://www.phys.hwii.edu/~vne/phys7-sp1/physics7.html Remindes: 1) Assignment #8 vilble ) Chpte 8 this week Lectue 3 iot-svt s Lw (Continued) θ d θ P R R θ R d θ d Mgnetic Fields fom long

### Physics 11b Lecture #11

Physics 11b Lectue #11 Mgnetic Fields Souces of the Mgnetic Field S&J Chpte 9, 3 Wht We Did Lst Time Mgnetic fields e simil to electic fields Only diffeence: no single mgnetic pole Loentz foce Moving chge

### Winter 2004 OSU Sources of Magnetic Fields 1 Chapter 32

Winte 4 OSU 1 Souces Of Mgnetic Fields We lened two wys to clculte Electic Field Coulomb's Foce de 4 E da 1 dq Q enc ˆ ute Foce Clcultion High symmety Wht e the nlogous equtions fo the Mgnetic Field? Winte

### ( ) ( ) ( ) ( ) ( ) # B x ( ˆ i ) ( ) # B y ( ˆ j ) ( ) # B y ("ˆ ( ) ( ) ( (( ) # ("ˆ ( ) ( ) ( ) # B ˆ z ( k )

Emple 1: A positie chge with elocit is moing though unifom mgnetic field s shown in the figues below. Use the ight-hnd ule to detemine the diection of the mgnetic foce on the chge. Emple 1 ˆ i = ˆ ˆ i

### Solutions to Midterm Physics 201

Solutions to Midtem Physics. We cn conside this sitution s supeposition of unifomly chged sphee of chge density ρ nd dius R, nd second unifomly chged sphee of chge density ρ nd dius R t the position of

### Electric Potential. and Equipotentials

Electic Potentil nd Euipotentils U Electicl Potentil Review: W wok done y foce in going fom to long pth. l d E dl F W dl F θ Δ l d E W U U U Δ Δ l d E W U U U U potentil enegy electic potentil Potentil

### 3.1 Magnetic Fields. Oersted and Ampere

3.1 Mgnetic Fields Oested nd Ampee The definition of mgnetic induction, B Fields of smll loop (dipole) Mgnetic fields in mtte: ) feomgnetism ) mgnetiztion, (M ) c) mgnetic susceptiility, m d) mgnetic field,

### Electric Field F E. q Q R Q. ˆ 4 r r - - Electric field intensity depends on the medium! origin

1 1 Electic Field + + q F Q R oigin E 0 0 F E ˆ E 4 4 R q Q R Q - - Electic field intensity depends on the medium! Electic Flux Density We intoduce new vecto field D independent of medium. D E So, electic

### Chapter 21: Electric Charge and Electric Field

Chpte 1: Electic Chge nd Electic Field Electic Chge Ancient Gees ~ 600 BC Sttic electicit: electic chge vi fiction (see lso fig 1.1) (Attempted) pith bll demonsttion: inds of popeties objects with sme

### General Physics II. number of field lines/area. for whole surface: for continuous surface is a whole surface

Genel Physics II Chpte 3: Guss w We now wnt to quickly discuss one of the moe useful tools fo clculting the electic field, nmely Guss lw. In ode to undestnd Guss s lw, it seems we need to know the concept

### ELECTRO - MAGNETIC INDUCTION

NTRODUCTON LCTRO - MAGNTC NDUCTON Whenee mgnetic flu linked with cicuit chnges, n e.m.f. is induced in the cicuit. f the cicuit is closed, cuent is lso induced in it. The e.m.f. nd cuent poduced lsts s

### (A) 6.32 (B) 9.49 (C) (D) (E) 18.97

Univesity of Bhin Physics 10 Finl Exm Key Fll 004 Deptment of Physics 13/1/005 8:30 10:30 e =1.610 19 C, m e =9.1110 31 Kg, m p =1.6710 7 Kg k=910 9 Nm /C, ε 0 =8.8410 1 C /Nm, µ 0 =4π10 7 T.m/A Pt : 10

### This immediately suggests an inverse-square law for a "piece" of current along the line.

Electomgnetic Theoy (EMT) Pof Rui, UNC Asheville, doctophys on YouTube Chpte T Notes The iot-svt Lw T nvese-sque Lw fo Mgnetism Compe the mgnitude of the electic field t distnce wy fom n infinite line

### MAGNETIC EFFECT OF CURRENT & MAGNETISM

TODUCTO MAGETC EFFECT OF CUET & MAGETM The molecul theo of mgnetism ws given b Webe nd modified lte b Ewing. Oested, in 18 obseved tht mgnetic field is ssocited with n electic cuent. ince, cuent is due

### Collection of Formulas

Collection of Fomuls Electomgnetic Fields EITF8 Deptment of Electicl nd Infomtion Technology Lund Univesity, Sweden August 8 / ELECTOSTATICS field point '' ' Oigin ' Souce point Coulomb s Lw The foce F

### Sources of Magnetic Fields (chap 28)

Souces of Magnetic Fields (chap 8) In chapte 7, we consideed the magnetic field effects on a moving chage, a line cuent and a cuent loop. Now in Chap 8, we conside the magnetic fields that ae ceated by

### 16.1 Permanent magnets

Unit 16 Magnetism 161 Pemanent magnets 16 The magnetic foce on moving chage 163 The motion of chaged paticles in a magnetic field 164 The magnetic foce exeted on a cuent-caying wie 165 Cuent loops and

### Physics 1502: Lecture 2 Today s Agenda

1 Lectue 1 Phsics 1502: Lectue 2 Tod s Agend Announcements: Lectues posted on: www.phs.uconn.edu/~cote/ HW ssignments, solutions etc. Homewok #1: On Mstephsics this Fid Homewoks posted on Msteingphsics

### Magnetic Fields Due to Currents

PH -C Fall 1 Magnetic Fields Due to Cuents Lectue 14 Chapte 9 (Halliday/esnick/Walke, Fundamentals of Physics 8 th edition) 1 Chapte 9 Magnetic Fields Due to Cuents In this chapte we will exploe the elationship

### Continuous Charge Distributions

Continuous Chge Distibutions Review Wht if we hve distibution of chge? ˆ Q chge of distibution. Q dq element of chge. d contibution to due to dq. Cn wite dq = ρ dv; ρ is the chge density. = 1 4πε 0 qi

### Ch 30 - Sources of Magnetic Field! The Biot-Savart Law! = k m. r 2. Example 1! Example 2!

Ch 30 - Souces of Magnetic Field 1.) Example 1 Detemine the magnitude and diection of the magnetic field at the point O in the diagam. (Cuent flows fom top to bottom, adius of cuvatue.) Fo staight segments,

### ELECTROSTATICS. 4πε0. E dr. The electric field is along the direction where the potential decreases at the maximum rate. 5. Electric Potential Energy:

LCTROSTATICS. Quntiztion of Chge: Any chged body, big o smll, hs totl chge which is n integl multile of e, i.e. = ± ne, whee n is n intege hving vlues,, etc, e is the chge of electon which is eul to.6

### MAGNETIC FIELD INTRODUCTION

MAGNETIC FIELD INTRODUCTION It was found when a magnet suspended fom its cente, it tends to line itself up in a noth-south diection (the compass needle). The noth end is called the Noth Pole (N-pole),

### School of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007

School of Electicl nd Compute Engineeing, Conell Univesity ECE 303: Electomgnetic Fields nd Wves Fll 007 Homewok 3 Due on Sep. 14, 007 by 5:00 PM Reding Assignments: i) Review the lectue notes. ii) Relevnt

### CHAPTER 18: ELECTRIC CHARGE AND ELECTRIC FIELD

ollege Physics Student s Mnul hpte 8 HAPTR 8: LTRI HARG AD LTRI ILD 8. STATI LTRIITY AD HARG: OSRVATIO O HARG. ommon sttic electicity involves chges nging fom nnocoulombs to micocoulombs. () How mny electons

### A moving charged particle creates a magnetic field vector at every point in space except at its position.

1 Pat 3: Magnetic Foce 3.1: Magnetic Foce & Field A. Chaged Paticles A moving chaged paticle ceates a magnetic field vecto at evey point in space ecept at its position. Symbol fo Magnetic Field mks units

### Algebra Based Physics. Gravitational Force. PSI Honors universal gravitation presentation Update Fall 2016.notebookNovember 10, 2016

Newton's Lw of Univesl Gvittion Gvittionl Foce lick on the topic to go to tht section Gvittionl Field lgeb sed Physics Newton's Lw of Univesl Gvittion Sufce Gvity Gvittionl Field in Spce Keple's Thid Lw

### Unit 6. Magnetic forces

Unit 6 Mgnetic foces 6.1 ntoduction. Mgnetic field 6. Mgnetic foces on moving electic chges 6. oce on conducto with cuent. 6.4 Action of unifom mgnetic field on flt cuent-cying loop. Mgnetic moment. Electic

### Magnetic fields (origins) CHAPTER 27 SOURCES OF MAGNETIC FIELD. Permanent magnets. Electric currents. Magnetic field due to a moving charge.

Magnetic fields (oigins) CHAPTER 27 SOURCES OF MAGNETC FELD Magnetic field due to a moving chage. Electic cuents Pemanent magnets Magnetic field due to electic cuents Staight wies Cicula coil Solenoid

### U>, and is negative. Electric Potential Energy

Electic Potentil Enegy Think of gvittionl potentil enegy. When the lock is moved veticlly up ginst gvity, the gvittionl foce does negtive wok (you do positive wok), nd the potentil enegy (U) inceses. When

### School of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007

School of Electicl nd Compute Engineeing, Conell Univesity ECE 303: Electomgnetic Fields nd Wves Fll 007 Homewok 4 Due on Sep. 1, 007 by 5:00 PM Reding Assignments: i) Review the lectue notes. ii) Relevnt

### Lecture 11: Potential Gradient and Capacitor Review:

Lectue 11: Potentil Gdient nd Cpcito Review: Two wys to find t ny point in spce: Sum o Integte ove chges: q 1 1 q 2 2 3 P i 1 q i i dq q 3 P 1 dq xmple of integting ove distiution: line of chge ing of

### Sources of the Magnetic Field. Moving charges currents Ampere s Law Gauss Law in magnetism Magnetic materials

Souces of the Magnetic Field Moving chages cuents Ampee s Law Gauss Law in magnetism Magnetic mateials Biot-Savat Law ˆ ˆ θ ds P db out I db db db db ds ˆ 1 I P db in db db ds sinθ db μ 4 π 0 Ids ˆ B μ0i

### PHY 114 A General Physics II 11 AM-12:15 PM TR Olin 101

PHY 114 A Geneal Physics II 11 AM-1:15 PM TR Olin 11 Plan fo Lectue 1 Chaptes 3): Souces of Magnetic fields 1. Pemanent magnets.biot-savat Law; magnetic fields fom a cuent-caying wie 3.Ampee Law 4.Magnetic

### 3-Axis Vector Magnet: Construction and Characterisation of Split Coils at RT. Semester Project Petar Jurcevic

3-Axis Vecto Magnet: Constuction and Chaacteisation of Split Coils at RT Semeste Poject Peta Jucevic Outline Field Calculation and Simulation Constuction Details Field Calculations Chaacteization at RT

### Magnetic Field. Conference 6. Physics 102 General Physics II

Physics 102 Confeence 6 Magnetic Field Confeence 6 Physics 102 Geneal Physics II Monday, Mach 3d, 2014 6.1 Quiz Poblem 6.1 Think about the magnetic field associated with an infinite, cuent caying wie.

### Magnetic Field of a Wire

Magnetic Field of a Wie Fundamental Laws fo Calculating B-field Biot-Savat Law (long method, but woks always) Ampee s Law (high symmety) B-Field of a Staight Wie Fo a thin staight conducto caying cuent

### Homework 3 MAE 118C Problems 2, 5, 7, 10, 14, 15, 18, 23, 30, 31 from Chapter 5, Lamarsh & Baratta. The flux for a point source is:

. Homewok 3 MAE 8C Poblems, 5, 7, 0, 4, 5, 8, 3, 30, 3 fom Chpte 5, msh & Btt Point souces emit nuetons/sec t points,,, n 3 fin the flux cuent hlf wy between one sie of the tingle (blck ot). The flux fo

### Conventional Current B = In some materials current moving charges are positive: Ionic solution Holes in some materials (same charge as electron but +)

Conventional Cuent In some mateials cuent moving chages ae positive: Ionic solution Holes in some mateials (same chage as electon but +) Obseving magnetic field aound coppe wie: Can we tell whethe the

### π,π is the angle FROM a! TO b

Mth 151: 1.2 The Dot Poduct We hve scled vectos (o, multiplied vectos y el nume clled scl) nd dded vectos (in ectngul component fom). Cn we multiply vectos togethe? The nswe is YES! In fct, thee e two

### Physics Spring 2012 Announcements: Mar 07, 2012

Physics 00 - Sping 01 Announcements: Ma 07, 01 HW#6 due date has been extended to the moning of Wed. Ma 1. Test # (i. Ma ) will cove only chaptes 0 and 1 All of chapte will be coveed in Test #4!!! Test

### PX3008 Problem Sheet 1

PX38 Poblem Sheet 1 1) A sphee of dius (m) contins chge of unifom density ρ (Cm -3 ). Using Guss' theoem, obtin expessions fo the mgnitude of the electic field (t distnce fom the cente of the sphee) in

### Chapter 2: Electric Field

P 6 Genel Phsics II Lectue Outline. The Definition of lectic ield. lectic ield Lines 3. The lectic ield Due to Point Chges 4. The lectic ield Due to Continuous Chge Distibutions 5. The oce on Chges in

### Calculate the electric potential at B d2=4 m Calculate the electric potential at A d1=3 m 3 m 3 m

MTE : Ch 13 5:3-7pm on Oct 31 ltenate Exams: Wed Ch 13 6:3pm-8:pm (people attending the altenate exam will not be allowed to go out of the oom while othes fom pevious exam ae still aound) Thu @ 9:-1:3

### DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING FLUID MECHANICS III Solutions to Problem Sheet 3

DEPATMENT OF CIVIL AND ENVIONMENTAL ENGINEEING FLID MECHANICS III Solutions to Poblem Sheet 3 1. An tmospheic vote is moelle s combintion of viscous coe otting s soli boy with ngul velocity Ω n n iottionl

### 10 m, so the distance from the Sun to the Moon during a solar eclipse is. The mass of the Sun, Earth, and Moon are = =

Chpte 1 nivesl Gvittion 11 *P1. () The un-th distnce is 1.4 nd the th-moon 8 distnce is.84, so the distnce fom the un to the Moon duing sol eclipse is 11 8 11 1.4.84 = 1.4 The mss of the un, th, nd Moon

### Answers to test yourself questions

Answes to test youself questions opic Descibing fields Gm Gm Gm Gm he net field t is: g ( d / ) ( 4d / ) d d Gm Gm Gm Gm Gm Gm b he net potentil t is: V d / 4d / d 4d d d V e 4 7 9 49 J kg 7 7 Gm d b E

### STD: XI MATHEMATICS Total Marks: 90. I Choose the correct answer: ( 20 x 1 = 20 ) a) x = 1 b) x =2 c) x = 3 d) x = 0

STD: XI MATHEMATICS Totl Mks: 90 Time: ½ Hs I Choose the coect nswe: ( 0 = 0 ). The solution of is ) = b) = c) = d) = 0. Given tht the vlue of thid ode deteminnt is then the vlue of the deteminnt fomed

### TUTORIAL 9. Static magnetic field

TUTOIAL 9 Static magnetic field Vecto magnetic potential Null Identity % & %\$ A # Fist postulation # " B such that: Vecto magnetic potential Vecto Poisson s equation The solution is: " Substitute it into

### Electrostatics. 1. Show does the force between two point charges change if the dielectric constant of the medium in which they are kept increase?

Electostatics 1. Show does the foce between two point chages change if the dielectic constant of the medium in which they ae kept incease? 2. A chaged od P attacts od R whee as P epels anothe chaged od

### Course Updates. Reminders: 1) Assignment #8 will be able to do after today. 2) Finish Chapter 28 today. 3) Quiz next Friday

Couse Updates http://www.phys.hawaii.edu/~vane/phys272-sp10/physics272.html Remindes: 1) Assignment #8 will be able to do afte today 2) Finish Chapte 28 today 3) Quiz next Fiday 4) Review of 3 ight-hand

### Review for 2 nd Midterm

Review fo 2 nd Midtem Midtem-2! Wednesday Octobe 29 at 6pm Section 1 N100 BCC (Business College) Section 2 158 NR (Natual Resouces) Allowed one sheet of notes (both sides) and calculato Coves Chaptes 27-31

### Physics 122, Fall October 2012

hsics 1, Fall 1 3 Octobe 1 Toda in hsics 1: finding Foce between paallel cuents Eample calculations of fom the iot- Savat field law Ampèe s Law Eample calculations of fom Ampèe s law Unifom cuents in conductos?

### Prof. Anchordoqui Problems set # 12 Physics 169 May 12, 2015

Pof. Anchodoqui Poblems set # 12 Physics 169 My 12, 2015 1. Two concentic conducting sphees of inne nd oute dii nd b, espectively, cy chges ±Q. The empty spce between the sphees is hlf-filled by hemispheicl

### 858 Questions 1. O (iii) (iv) 11. O 2. O (i) (ii) 12. O 3. O (i) 13. (ii) 14. O 5. O 6. O 15. O O (i) (ii)

858 Chpte 30 Souces of the Mgnetic Field Questions denotes nswe vilble in Student Solutions Mnul/Stud Guide; O denotes objective question 1. O Wht cetes mgnetic field? Choose eve coect nswe. () sttion

### Chapter 22 The Electric Field II: Continuous Charge Distributions

Chpte The lectic Field II: Continuous Chge Distibutions Conceptul Poblems [SSM] Figue -7 shows n L-shped object tht hs sides which e equl in length. Positive chge is distibuted unifomly long the length

### Unit 7: Sources of magnetic field

Unit 7: Souces of magnetic field Oested s expeiment. iot and Savat s law. Magnetic field ceated by a cicula loop Ampèe s law (A.L.). Applications of A.L. Magnetic field ceated by a: Staight cuent-caying

### Physics 604 Problem Set 1 Due Sept 16, 2010

Physics 64 Polem et 1 Due ept 16 1 1) ) Inside good conducto the electic field is eo (electons in the conducto ecuse they e fee to move move in wy to cncel ny electic field impessed on the conducto inside

### Electrostatics (Electric Charges and Field) #2 2010

Electic Field: The concept of electic field explains the action at a distance foce between two chaged paticles. Evey chage poduces a field aound it so that any othe chaged paticle expeiences a foce when

### How Electric Currents Interact with Magnetic Fields

How Electic Cuents nteact with Magnetic Fields 1 Oested and Long Wies wote these notes to help ou with vaious diectional ules, and the equivalence between the magnetism of magnets and the magnets of electic

### Review. Electrostatic. Dr. Ray Kwok SJSU

Review Electostatic D. Ray Kwok SJSU Paty Balloons Coulomb s Law F e q q k 1 Coulomb foce o electical foce. (vecto) Be caeful on detemining the sign & diection. k 9 10 9 (N m / C ) k 1 4πε o k is the Coulomb

### Work, Potential Energy, Conservation of Energy. the electric forces are conservative: ur r

Wok, Potentil Enegy, Consevtion of Enegy the electic foces e consevtive: u Fd = Wok, Potentil Enegy, Consevtion of Enegy b b W = u b b Fdl = F()[ d + \$ \$ dl ] = F() d u Fdl = the electic foces e consevtive

### ( ) Make-up Tests. From Last Time. Electric Field Flux. o The Electric Field Flux through a bit of area is

Mon., 3/23 Wed., 3/25 Thus., 3/26 Fi., 3/27 Mon., 3/30 Tues., 3/31 21.4-6 Using Gauss s & nto to Ampee s 21.7-9 Maxwell s, Gauss s, and Ampee s Quiz Ch 21, Lab 9 Ampee s Law (wite up) 22.1-2,10 nto to

### The Law of Biot-Savart & RHR P θ

The Law of iot-savat & RHR P R dx x Jean-aptiste iot élix Savat Phys 122 Lectue 19 G. Rybka Recall: Potential Enegy of Dipole Wok equied to otate a cuentcaying loop in a magnetic field Potential enegy

### in a uniform magnetic flux density B = Boa z. (a) Show that the electron moves in a circular path. (b) Find the radius r o

6. THE TATC MAGNETC FELD 6- LOENTZ FOCE EQUATON Lorent force eqution F = Fe + Fm = q ( E + v B ) Exmple 6- An electron hs n initil velocity vo = vo y in uniform mgnetic flux density B = Bo. () how tht

### 1. The sphere P travels in a straight line with speed

1. The sphee P tels in stight line with speed = 10 m/s. Fo the instnt depicted, detemine the coesponding lues of,,,,, s mesued eltie to the fixed Oxy coodinte system. (/134) + 38.66 1.34 51.34 10sin 3.639

### 13.5. Torsion of a curve Tangential and Normal Components of Acceleration

13.5 osion of cuve ngentil nd oml Components of Acceletion Recll: Length of cuve '( t) Ac length function s( t) b t u du '( t) Ac length pmetiztion ( s) with '( s) 1 '( t) Unit tngent vecto '( t) Cuvtue:

### \$ i. !((( dv vol. Physics 8.02 Quiz One Equations Fall q 1 q 2 r 2 C = 2 C! V 2 = Q 2 2C F = 4!" or. r ˆ = points from source q to observer

Physics 8.0 Quiz One Equations Fall 006 F = 1 4" o q 1 q = q q ˆ 3 4" o = E 4" o ˆ = points fom souce q to obseve 1 dq E = # ˆ 4" 0 V "## E "d A = Q inside closed suface o d A points fom inside to V =

### ( ) ( ) Physics 111. Lecture 13 (Walker: Ch ) Connected Objects Circular Motion Centripetal Acceleration Centripetal Force Sept.

Physics Lectue 3 (Wlke: Ch. 6.4-5) Connected Objects Cicul Motion Centipetl Acceletion Centipetl Foce Sept. 30, 009 Exmple: Connected Blocks Block of mss m slides on fictionless tbletop. It is connected

### Designing a Sine-Coil for Measurement of Plasma Displacements in IR-T1 Tokamak

Designing a Sine-Coil fo Measuement of Plasma Displacements in IR-T Tokamak Pejman Khoshid, M. Razavi, M. Ghoanneviss, M. Molaii, A. TalebiTahe, R. Avin, S. Mohammadi and A. NikMohammadi Dept. of Physics,

### Electricity & Magnetism Lecture 6: Electric Potential

Electicity & Mgnetism Lectue 6: Electic Potentil Tody s Concept: Electic Potenl (Defined in tems of Pth Integl of Electic Field) Electicity & Mgnesm Lectue 6, Slide Stuff you sked bout:! Explin moe why

### ( ) ( )( ) ˆ. Homework #8. Chapter 27 Magnetic Fields II.

Homewok #8. hapte 7 Magnetic ields. 6 Eplain how ou would modif Gauss s law if scientists discoveed that single, isolated magnetic poles actuall eisted. Detemine the oncept Gauss law fo magnetism now eads

### Chapter 7 Steady Magnetic Field. september 2016 Microwave Laboratory Sogang University

Chpter 7 Stedy Mgnetic Field september 2016 Microwve Lbortory Sogng University Teching point Wht is the mgnetic field? Biot-Svrt s lw: Coulomb s lw of Mgnetic field Stedy current: current flow is independent

### Section 35 SHM and Circular Motion

Section 35 SHM nd Cicul Motion Phsics 204A Clss Notes Wht do objects do? nd Wh do the do it? Objects sometimes oscillte in simple hmonic motion. In the lst section we looed t mss ibting t the end of sping.

### Chapter 25: Current, Resistance and Electromotive Force. Charge carrier motion in a conductor in two parts

Chpte 5: Cuent, esistnce nd Electomotive Foce Chge cie motion in conducto in two pts Constnt Acceletion F m qe ndomizing Collisions (momentum, enegy) =>esulting Motion Avege motion = Dift elocity = v d

### Chapter 4 Kinematics in Two Dimensions

D Kinemtic Quntities Position nd Velocit Acceletion Applictions Pojectile Motion Motion in Cicle Unifom Cicul Motion Chpte 4 Kinemtics in Two Dimensions D Motion Pemble In this chpte, we ll tnsplnt the

### Magnetostatics. Magnetic Forces. = qu. Biot-Savart Law H = Gauss s Law for Magnetism. Ampere s Law. Magnetic Properties of Materials. Inductance M.

Magnetic Foces Biot-Savat Law Gauss s Law fo Magnetism Ampee s Law Magnetic Popeties of Mateials nductance F m qu d B d R 4 R B B µ 0 J Magnetostatics M. Magnetic Foces The electic field E at a point in

### Physics 505 Fall 2005 Midterm Solutions. This midterm is a two hour open book, open notes exam. Do all three problems.

Physics 55 Fll 5 Midtem Solutions This midtem is two hou open ook, open notes exm. Do ll thee polems. [35 pts] 1. A ectngul ox hs sides of lengths, nd c z x c [1] ) Fo the Diichlet polem in the inteio

### Gauss s Law: Circuits

Gauss s Law: Cicuits Can we have excess chage inside in steady state? E suface nˆ A q inside E nˆ A E nˆ A left _ suface ight _ suface q inside 1 Gauss s Law: Junction Between two Wies n 2

### Chapter 26: Magnetism: Force and Field

Chapte 6: Magnetism: Foce and Field Magnets Magnetism Magnetic foces Magnetism Magnetic field of Eath Magnetism Magnetism Magnetic monopoles? Pehaps thee exist magnetic chages, just like electic chages.

### Objectives: After finishing this unit you should be able to:

lectic Field 7 Objectives: Afte finishing this unit you should be able to: Define the electic field and explain what detemines its magnitude and diection. Wite and apply fomulas fo the electic field intensity

### Chapter 25: Current, Resistance and Electromotive Force. ~10-4 m/s Typical speeds ~ 10 6 m/s

Chpte 5: Cuent, esistnce nd lectomotive Foce Chge cie motion in conducto in two pts Constnt Acceletion F m q ndomizing Collisions (momentum, enegy) >esulting Motion http://phys3p.sl.psu.edu/phys_nim/m/ndom_wlk.vi

### (a) Counter-Clockwise (b) Clockwise ()N (c) No rotation (d) Not enough information

m m m00 kg dult, m0 kg bby. he seesw stts fom est. Which diection will it ottes? ( Counte-Clockwise (b Clockwise ( (c o ottion ti (d ot enough infomtion Effect of Constnt et oque.3 A constnt non-zeo toque

### Chapter 4 Two-Dimensional Motion

D Kinemtic Quntities Position nd Velocit Acceletion Applictions Pojectile Motion Motion in Cicle Unifom Cicul Motion Chpte 4 Two-Dimensionl Motion D Motion Pemble In this chpte, we ll tnsplnt the conceptul

### Version 001 HW#6 - Electromagnetism arts (00224) 1

Version 001 HW#6 - Electromgnetism rts (00224) 1 This print-out should hve 11 questions. Multiple-choice questions my continue on the next column or pge find ll choices efore nswering. rightest Light ul

### r = (0.250 m) + (0.250 m) r = m = = ( N m / C )

ELECTIC POTENTIAL IDENTIFY: Apply Eq() to clculte the wok The electic potentil enegy of pi of point chges is given y Eq(9) SET UP: Let the initil position of q e point nd the finl position e point, s shown

### CHAPTER 25 ELECTRIC POTENTIAL

CHPTE 5 ELECTIC POTENTIL Potential Diffeence and Electic Potential Conside a chaged paticle of chage in a egion of an electic field E. This filed exets an electic foce on the paticle given by F=E. When

### Mark Scheme (Results) January 2008

Mk Scheme (Results) Jnuy 00 GCE GCE Mthemtics (6679/0) Edecel Limited. Registeed in Englnd nd Wles No. 4496750 Registeed Office: One90 High Holbon, London WCV 7BH Jnuy 00 6679 Mechnics M Mk Scheme Question

### The Formulas of Vector Calculus John Cullinan

The Fomuls of Vecto lculus John ullinn Anlytic Geomety A vecto v is n n-tuple of el numbes: v = (v 1,..., v n ). Given two vectos v, w n, ddition nd multipliction with scl t e defined by Hee is bief list

### Energy Dissipation Gravitational Potential Energy Power

Lectue 4 Chpte 8 Physics I 0.8.03 negy Dissiption Gvittionl Potentil negy Powe Couse wesite: http://fculty.uml.edu/andiy_dnylov/teching/physicsi Lectue Cptue: http://echo360.uml.edu/dnylov03/physicsfll.html

### Physics 2020, Spring 2005 Lab 5 page 1 of 8. Lab 5. Magnetism

Physics 2020, Sping 2005 Lab 5 page 1 of 8 Lab 5. Magnetism PART I: INTRODUCTION TO MAGNETS This week we will begin wok with magnets and the foces that they poduce. By now you ae an expet on setting up

### Chapter 24. Gauss s Law

Chpte 24 Guss s Lw CHAPTR OUTLIN 24.1 lectic Flux 24.2 Guss s Lw 24.3 Appliction of Guss s Lw to Vious Chge Distibutions 24.4 Conductos in lectosttic uilibium 24.5 Foml Deivtion of Guss s Lw In tble-top

### F Q E v B MAGNETOSTATICS. Creation of magnetic field B. Effect of B on a moving charge. On moving charges only. Stationary and moving charges

MAGNETOSTATICS Ceation of magnetic field. Effect of on a moving chage. Take the second case: F Q v mag On moving chages only F QE v Stationay and moving chages dw F dl Analysis on F mag : mag mag Qv. vdt

### Chapter 31 Faraday s Law

Chapte 31 Faaday s Law Change oving --> cuent --> agnetic field (static cuent --> static agnetic field) The souce of agnetic fields is cuent. The souce of electic fields is chage (electic onopole). Altenating

Faaday s Law (continued) What causes cuent to flow in wie? Answe: an field in the wie. A changing magnetic flux not only causes an MF aound a loop but an induced electic field. Can wite Faaday s Law: ε

### Physics 111. Uniform circular motion. Ch 6. v = constant. v constant. Wednesday, 8-9 pm in NSC 128/119 Sunday, 6:30-8 pm in CCLIR 468

ics Announcements dy, embe 28, 2004 Ch 6: Cicul Motion - centipetl cceletion Fiction Tension - the mssless sting Help this week: Wednesdy, 8-9 pm in NSC 128/119 Sundy, 6:30-8 pm in CCLIR 468 Announcements

### anubhavclasses.wordpress.com CBSE Solved Test Papers PHYSICS Class XII Chapter : Electrostatics

CBS Solved Test Papes PHYSICS Class XII Chapte : lectostatics CBS TST PAPR-01 CLASS - XII PHYSICS (Unit lectostatics) 1. Show does the foce between two point chages change if the dielectic constant of

### Chapter 7. Kleene s Theorem. 7.1 Kleene s Theorem. The following theorem is the most important and fundamental result in the theory of FA s:

Chpte 7 Kleene s Theoem 7.1 Kleene s Theoem The following theoem is the most impotnt nd fundmentl esult in the theoy of FA s: Theoem 6 Any lnguge tht cn e defined y eithe egul expession, o finite utomt,