The Law of Biot-Savart & RHR P θ

Size: px
Start display at page:

Download "The Law of Biot-Savart & RHR P θ"

Transcription

1 The Law of iot-savat & RHR P R dx x Jean-aptiste iot élix Savat Phys 122 Lectue 19 G. Rybka

2 Recall: Potential Enegy of Dipole Wok equied to otate a cuentcaying loop in a magnetic field Potential enegy U = - Wok done by field leads to U τd Þ U = µ x µ. With U = 0 at = 90 (whee toque is maximum)

3 Plotting U = -µ U = +µcos U = 0 U = µcos WHCH ORENTATON HAS THE MOST POTNTAL ENERGY? U()

4 Now some new stuff but fist

5 Right-Hand-Rule Pe-Summay = qv = L τ = = µ d = τ ˆ 0 d s 2 µ 4π t is going to get easie

6 Calculation of Electic ield Two ways to calculate the Electic ield: Coulomb's Law: E = 1 πε q " "ute foce" Gauss' Law ε 0 E ds = q "High symmety" What ae the analogous equations fo the Magnetic ield?

7 Calculation of Magnetic ield Two ways to calculate the Magnetic ield: iot-savat Law: d = µ 0 dl 4π 3 "ute foce" Ampee's Law dl = µ 0 "High symmety" These ae the analogous equations fo the Magnetic ield

8 iot-savat Law bits and pieces dl Diffeential magnetic field fom a diffeential cuent element d = X d µ 4π 0 dl ˆ 2 µ = 4π Tm/A pemeability of fee space, ield hee? Apply RHR fom above ield points into the page ntegate along the whole wie So, the magnetic field ciculates aound the wie

9 Magnetic ield of Staight Wie Calculate field at point P using iot-savat Law: µ dx d = 0 4π 3 Which way is? à RHR + µ dx = d = 0 ( ) sin 4π 3 Rewite in tems of R,: dx P is out of page R x R = sin Þ tan = R x Þ x = Rcot dx = R 1 d 2 sin Þ dx(sin ) 2 = sind R

10 Magnetic ield of Staight Wie π 0 d = µ 0 4 sin π R dx P R is out of page x π µ = 0 4πR 0 sind Þ = µ 0 [ ] 4πR cos π 0 = µ 0 2 πr

11 How do we check this esult? i.e. that we expect fom wie to be popotional to /R? Measue ORCE on cuent-caying wie due to the magnetic field PRODUCED by ANOTHER cuent caying wie a d b How does foce depend on cuents and sepaation?

12 oce on 2 Paallel Cuent-Caying Wies Calculate foce on length L of wie b due to field of wie a: The field at b due to a is given by: Calculate foce on length L of wie a due to field of wie b: The field at a due to b is given by: d a = µ π a 0 2 L d b a L d b a Þ oce on b = d L L b a a b b π µ 2 0 = = d b = µ π b 0 2 Þ oce on a = d L L b a b a a π µ 2 0 = =

13 oce etween Cuent-Caying Wies towads us d = 2 L Anothe towads us = µ o L 2πd Conclusion: Cuents in same diection attact towads us d Anothe away fom us Conclusion: Cuents in opposite diection epel

14 A long staight wie is caying cuent fom left to ight. Two identical chages ae moving with equal speed. Compae the magnitude of the foce on chage a moving diectly to the ight, to the magnitude of the foce on chage b moving up and to the ight at the instant shown (i.e. same distance fom the wie). v v (a) (b) A) a > b ) a = b C) a < b Clicke = qv = qvsin Same q, v, and (=90) ut, oces ae in diffeent diections

15 Clicke Two long wies cay opposite cuent x What is the diection of the magnetic field above, and midway between the two wies caying cuent at the point maked X? A) Left ) Right C) Up D) Down E) Zeo x

16 CheckPoint 2 & 4 X What is the diection of the foce on wie 2 due to wie 1? A) Up ) Down C) nto Sceen D) Out of sceen E) Zeo What is the diection of the toque on wie 2 due to wie 1? A) Up ) Down C) nto Sceen D) Out of sceen E) Zeo Unifom foce at evey segment of wie No toque about any axis

17 Clicke A cuent flows in the positive y diection in an infinite wie;; a cuent also flows in the loop as shown in the diagam. What is x, net foce on the loop in the x- diection? y left X top ight (a) x < 0 (b) x = 0 (c) x > 0 bottom x Recall fom a pevious CLCKER that the net foce on a cuent loop in a constant magnetic field was zeo. Howeve, the magnetic field hee is not a constant field The diection of the magnetic field at the cuent loop is in the -z diection. The foces on the top and bottom segments of the loop DO indeed cancel The foces on the left and ight segments of the loop DO NOT cancel The left segment of the loop is in a lage magnetic field. Theefoe, left > ight

18 CheckPoint 7: What is the diection of the net foce on wie 2 due to wie 1? A) Up ) Down C) nto Sceen D) Out of sceen E) Zeo WHY? DRAW PCTURE

19 Conside oce on Symmetic Segments out of sceen into sceen Net oce is Zeo

20 CheckPoint 9: we ae basically guessing What about the toque? same pictue What is the diection of the toque on wie 2 due to wie A) 1? Up ) Down C) nto Sceen D) Out of sceen E) Zeo One Response: do not undestand toque on wies in scenaios such as this one. O eally at all. out of sceen into sceen Anothe: While the magnetic foces on futhe pats of wie 2 (those which ae not diectly pependicula to wie 1) add up to zeo fo tanslational puposes, they point in opposite diections about a single axis of otation (diectly above wie 1), and thus thee will be a net toque on wie 2. The toque will point upwads due to the diection of the foces elative to the distance they ae fom the axis.

21 Right Hand Rule Review 1. ANY CROSS PRODUCT = qv = L τ = = µ d = τ ˆ 0 d s 2 µ 4π 2. Diection of Magnetic Moment inges: Cuent in Loop Thumb: Magnetic Moment 3. Diection of Magnetic ield fom Wie inges: Magnetic ield Thumb: Cuent

Physics 2112 Unit 14

Physics 2112 Unit 14 Physics 2112 Unit 14 Today s Concept: What Causes Magnetic Fields d 0I ds ˆ 2 4 Unit 14, Slide 1 You Comments Can you give a summay fo eveything we use the ight hand ule fo? Wasn't too clea on this topic.

More information

Physics Spring 2012 Announcements: Mar 07, 2012

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

More information

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

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

More information

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

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

More information

16.1 Permanent magnets

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

More information

MAGNETIC FIELD INTRODUCTION

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),

More information

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

( ) 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

More information

Sources of Magnetic Fields (chap 28)

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

More information

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

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

More information

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

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

More information

Magnetic Field. Conference 6. Physics 102 General Physics II

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.

More information

( )( )( ) ( ) + ( ) ( ) ( )

( )( )( ) ( ) + ( ) ( ) ( ) 3.7. Moel: The magnetic fiel is that of a moving chage paticle. Please efe to Figue Ex3.7. Solve: Using the iot-savat law, 7 19 7 ( ) + ( ) qvsinθ 1 T m/a 1.6 1 C. 1 m/s sin135 1. 1 m 1. 1 m 15 = = = 1.13

More information

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

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

More information

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

( ) ( )( ) 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

More information

Physics 2B Chapter 22 Notes - Magnetic Field Spring 2018

Physics 2B Chapter 22 Notes - Magnetic Field Spring 2018 Physics B Chapte Notes - Magnetic Field Sping 018 Magnetic Field fom a Long Staight Cuent-Caying Wie In Chapte 11 we looked at Isaac Newton s Law of Gavitation, which established that a gavitational field

More information

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

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

More information

Unit 7: Sources of magnetic field

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

More information

Electrostatics (Electric Charges and Field) #2 2010

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

More information

Physics 122, Fall October 2012

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?

More information

21 MAGNETIC FORCES AND MAGNETIC FIELDS

21 MAGNETIC FORCES AND MAGNETIC FIELDS CHAPTER 1 MAGNETIC ORCES AND MAGNETIC IELDS ANSWERS TO OCUS ON CONCEPTS QUESTIONS 1. (d) Right-Hand Rule No. 1 gives the diection of the magnetic foce as x fo both dawings A and. In dawing C, the velocity

More information

Magnetic Field of a Wire

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

More information

CHAPTER 25 ELECTRIC POTENTIAL

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

More information

Magnetic Dipoles Challenge Problem Solutions

Magnetic Dipoles Challenge Problem Solutions Magnetic Dipoles Challenge Poblem Solutions Poblem 1: Cicle the coect answe. Conside a tiangula loop of wie with sides a and b. The loop caies a cuent I in the diection shown, and is placed in a unifom

More information

Section 26 The Laws of Rotational Motion

Section 26 The Laws of Rotational Motion Physics 24A Class Notes Section 26 The Laws of otational Motion What do objects do and why do they do it? They otate and we have established the quantities needed to descibe this motion. We now need to

More information

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

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,

More information

EM-2. 1 Coulomb s law, electric field, potential field, superposition q. Electric field of a point charge (1)

EM-2. 1 Coulomb s law, electric field, potential field, superposition q. Electric field of a point charge (1) EM- Coulomb s law, electic field, potential field, supeposition q ' Electic field of a point chage ( ') E( ) kq, whee k / 4 () ' Foce of q on a test chage e at position is ee( ) Electic potential O kq

More information

Magnetic Fields Due to Currents

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

More information

Today s Plan. Electric Dipoles. More on Gauss Law. Comment on PDF copies of Lectures. Final iclicker roll-call

Today s Plan. Electric Dipoles. More on Gauss Law. Comment on PDF copies of Lectures. Final iclicker roll-call Today s Plan lectic Dipoles Moe on Gauss Law Comment on PDF copies of Lectues Final iclicke oll-call lectic Dipoles A positive (q) and negative chage (-q) sepaated by a small distance d. lectic dipole

More information

THE MAGNETIC FIELD. This handout covers: The magnetic force between two moving charges. The magnetic field, B, and magnetic field lines

THE MAGNETIC FIELD. This handout covers: The magnetic force between two moving charges. The magnetic field, B, and magnetic field lines EM 005 Handout 7: The Magnetic ield 1 This handout coes: THE MAGNETIC IELD The magnetic foce between two moing chages The magnetic field,, and magnetic field lines Magnetic flux and Gauss s Law fo Motion

More information

$ 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

$ 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 =

More information

Chapter 4. Newton s Laws of Motion

Chapter 4. Newton s Laws of Motion Chapte 4 Newton s Laws of Motion 4.1 Foces and Inteactions A foce is a push o a pull. It is that which causes an object to acceleate. The unit of foce in the metic system is the Newton. Foce is a vecto

More information

? this lecture. ? next lecture. What we have learned so far. a Q E F = q E a. F = q v B a. a Q in motion B. db/dt E. de/dt B.

? this lecture. ? next lecture. What we have learned so far. a Q E F = q E a. F = q v B a. a Q in motion B. db/dt E. de/dt B. PHY 249 Lectue Notes Chapte 32: Page 1 of 12 What we have leaned so fa a a F q a a in motion F q v a a d/ Ae thee othe "static" chages that can make -field? this lectue d/? next lectue da dl Cuve Cuve

More information

Physics 2212 GH Quiz #2 Solutions Spring 2016

Physics 2212 GH Quiz #2 Solutions Spring 2016 Physics 2212 GH Quiz #2 Solutions Sping 216 I. 17 points) Thee point chages, each caying a chage Q = +6. nc, ae placed on an equilateal tiangle of side length = 3. mm. An additional point chage, caying

More information

Last time RC circuits. Exam 2 is Tuesday Oct. 27 5:30-7 pm, Birge 145. Magnetic force on charged particle. Magnetic force on electric charges

Last time RC circuits. Exam 2 is Tuesday Oct. 27 5:30-7 pm, Birge 145. Magnetic force on charged particle. Magnetic force on electric charges Eam is Tuesda Oct. 7 5:0-7 pm, ige 45 Last time RC cicuits Students w / scheduled academic conflict please sta afte class TODAY to aange altenate time. Coes: all mateial since eam ook sections: Chap 7,

More information

2/26/2014. Magnetism. Chapter 20 Topics. Magnets and Magnetic Fields. Magnets and Magnetic Fields. Magnets and Magnetic Fields

2/26/2014. Magnetism. Chapter 20 Topics. Magnets and Magnetic Fields. Magnets and Magnetic Fields. Magnets and Magnetic Fields Magnets and Magnetic ields Magnetism Howee, if you cut a magnet in half, you don t get a noth pole and a south pole you get two smalle magnets. ectue otes Chapte 20 Topics Magnets and Magnetic ields Magnets

More information

Phys-272 Lecture 17. Motional Electromotive Force (emf) Induced Electric Fields Displacement Currents Maxwell s Equations

Phys-272 Lecture 17. Motional Electromotive Force (emf) Induced Electric Fields Displacement Currents Maxwell s Equations Phys-7 Lectue 17 Motional Electomotive Foce (emf) Induced Electic Fields Displacement Cuents Maxwell s Equations Fom Faaday's Law to Displacement Cuent AC geneato Magnetic Levitation Tain Review of Souces

More information

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

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

More information

Welcome to Physics 272

Welcome to Physics 272 Welcome to Physics 7 Bob Mose mose@phys.hawaii.edu http://www.phys.hawaii.edu/~mose/physics7.html To do: Sign into Masteing Physics phys-7 webpage Registe i-clickes (you i-clicke ID to you name on class-list)

More information

How Electric Currents Interact with Magnetic Fields

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

More information

MTE2 Wed 26, at 5:30-7:00 pm Ch2103 and SH 180. Contents of MTE2. Study chapters (no 32.6, 32.10, no 32.8 forces between wires)

MTE2 Wed 26, at 5:30-7:00 pm Ch2103 and SH 180. Contents of MTE2. Study chapters (no 32.6, 32.10, no 32.8 forces between wires) MTE Wed 6, at 5:30-7:00 pm Ch03 and SH 80 Contents of MTE Wok of the electic foce and potential enegy Electic Potential and ield Capacitos and capacitance Cuent and esistance, Ohm s la DC Cicuits and Kichoff

More information

Module 18: Outline. Magnetic Dipoles Magnetic Torques

Module 18: Outline. Magnetic Dipoles Magnetic Torques Module 18: Magnetic Dipoles 1 Module 18: Outline Magnetic Dipoles Magnetic Toques 2 IA nˆ I A Magnetic Dipole Moment μ 3 Toque on a Cuent Loop in a Unifom Magnetic Field 4 Poblem: Cuent Loop Place ectangula

More information

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

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

More information

Gauss Law. Physics 231 Lecture 2-1

Gauss Law. Physics 231 Lecture 2-1 Gauss Law Physics 31 Lectue -1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing

More information

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

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

More information

Faraday s Law. Faraday s Law. Faraday s Experiments. Faraday s Experiments. Magnetic Flux. Chapter 31. Law of Induction (emf( emf) Faraday s Law

Faraday s Law. Faraday s Law. Faraday s Experiments. Faraday s Experiments. Magnetic Flux. Chapter 31. Law of Induction (emf( emf) Faraday s Law Faaday s Law Faaday s Epeiments Chapte 3 Law of nduction (emf( emf) Faaday s Law Magnetic Flu Lenz s Law Geneatos nduced Electic fields Michael Faaday discoeed induction in 83 Moing the magnet induces

More information

Collaborative ASSIGNMENT Assignment 3: Sources of magnetic fields Solution

Collaborative ASSIGNMENT Assignment 3: Sources of magnetic fields Solution Electicity and Magnetism: PHY-04. 11 Novembe, 014 Collaboative ASSIGNMENT Assignment 3: Souces of magnetic fields Solution 1. a A conducto in the shape of a squae loop of edge length l m caies a cuent

More information

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

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

More information

Force between two parallel current wires and Newton s. third law

Force between two parallel current wires and Newton s. third law Foce between two paallel cuent wies and Newton s thid law Yannan Yang (Shanghai Jinjuan Infomation Science and Technology Co., Ltd.) Abstact: In this pape, the essence of the inteaction between two paallel

More information

Physics 2A Chapter 10 - Moment of Inertia Fall 2018

Physics 2A Chapter 10 - Moment of Inertia Fall 2018 Physics Chapte 0 - oment of netia Fall 08 The moment of inetia of a otating object is a measue of its otational inetia in the same way that the mass of an object is a measue of its inetia fo linea motion.

More information

Flux. Area Vector. Flux of Electric Field. Gauss s Law

Flux. Area Vector. Flux of Electric Field. Gauss s Law Gauss s Law Flux Flux in Physics is used to two distinct ways. The fist meaning is the ate of flow, such as the amount of wate flowing in a ive, i.e. volume pe unit aea pe unit time. O, fo light, it is

More information

Faraday s Law (continued)

Faraday s Law (continued) 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

More information

Algebra-based Physics II

Algebra-based Physics II lgebabased Physics II Chapte 19 Electic potential enegy & The Electic potential Why enegy is stoed in an electic field? How to descibe an field fom enegetic point of view? Class Website: Natual way of

More information

Review for 2 nd Midterm

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

More information

Voltage ( = Electric Potential )

Voltage ( = Electric Potential ) V-1 of 10 Voltage ( = lectic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage

More information

When a mass moves because of a force, we can define several types of problem.

When a mass moves because of a force, we can define several types of problem. Mechanics Lectue 4 3D Foces, gadient opeato, momentum 3D Foces When a mass moves because of a foce, we can define seveal types of poblem. ) When we know the foce F as a function of time t, F=F(t). ) When

More information

2. Electrostatics. Dr. Rakhesh Singh Kshetrimayum 8/11/ Electromagnetic Field Theory by R. S. Kshetrimayum

2. Electrostatics. Dr. Rakhesh Singh Kshetrimayum 8/11/ Electromagnetic Field Theory by R. S. Kshetrimayum 2. Electostatics D. Rakhesh Singh Kshetimayum 1 2.1 Intoduction In this chapte, we will study how to find the electostatic fields fo vaious cases? fo symmetic known chage distibution fo un-symmetic known

More information

Chapter 22: Electric Fields. 22-1: What is physics? General physics II (22102) Dr. Iyad SAADEDDIN. 22-2: The Electric Field (E)

Chapter 22: Electric Fields. 22-1: What is physics? General physics II (22102) Dr. Iyad SAADEDDIN. 22-2: The Electric Field (E) Geneal physics II (10) D. Iyad D. Iyad Chapte : lectic Fields In this chapte we will cove The lectic Field lectic Field Lines -: The lectic Field () lectic field exists in a egion of space suounding a

More information

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

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

More information

ELECTROMAGNETISM (CP2)

ELECTROMAGNETISM (CP2) Revision Lectue on ELECTROMAGNETISM (CP) Electostatics Magnetostatics Induction EM Waves based on pevious yeas Pelims questions State Coulomb s Law. Show how E field may be defined. What is meant by E

More information

Lab #0. Tutorial Exercises on Work and Fields

Lab #0. Tutorial Exercises on Work and Fields Lab #0 Tutoial Execises on Wok and Fields This is not a typical lab, and no pe-lab o lab epot is equied. The following execises will emind you about the concept of wok (fom 1130 o anothe intoductoy mechanics

More information

Physics NYB problem set 5 solution

Physics NYB problem set 5 solution Physics NY poblem set 5 solutions 1 Physics NY poblem set 5 solution Hello eveybody, this is ED. Hi ED! ED is useful fo dawing the ight hand ule when you don t know how to daw. When you have a coss poduct

More information

Charges, Coulomb s Law, and Electric Fields

Charges, Coulomb s Law, and Electric Fields Q&E -1 Chages, Coulomb s Law, and Electic ields Some expeimental facts: Expeimental fact 1: Electic chage comes in two types, which we call (+) and (). An atom consists of a heavy (+) chaged nucleus suounded

More information

Electromagnetism Physics 15b

Electromagnetism Physics 15b lectomagnetism Physics 15b Lectue #20 Dielectics lectic Dipoles Pucell 10.1 10.6 What We Did Last Time Plane wave solutions of Maxwell s equations = 0 sin(k ωt) B = B 0 sin(k ωt) ω = kc, 0 = B, 0 ˆk =

More information

Chapter 26: Magnetism: Force and Field

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.

More information

7.2. Coulomb s Law. The Electric Force

7.2. Coulomb s Law. The Electric Force Coulomb s aw Recall that chaged objects attact some objects and epel othes at a distance, without making any contact with those objects Electic foce,, o the foce acting between two chaged objects, is somewhat

More information

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

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

More information

PHYSICS 151 Notes for Online Lecture #20

PHYSICS 151 Notes for Online Lecture #20 PHYSICS 151 Notes fo Online Lectue #20 Toque: The whole eason that we want to woy about centes of mass is that we ae limited to looking at point masses unless we know how to deal with otations. Let s evisit

More information

FARADAY'S LAW. dates : No. of lectures allocated. Actual No. of lectures 3 9/5/09-14 /5/09

FARADAY'S LAW. dates : No. of lectures allocated. Actual No. of lectures 3 9/5/09-14 /5/09 FARADAY'S LAW No. of lectues allocated Actual No. of lectues dates : 3 9/5/09-14 /5/09 31.1 Faaday's Law of Induction In the pevious chapte we leaned that electic cuent poduces agnetic field. Afte this

More information

(Sample 3) Exam 1 - Physics Patel SPRING 1998 FORM CODE - A (solution key at end of exam)

(Sample 3) Exam 1 - Physics Patel SPRING 1998 FORM CODE - A (solution key at end of exam) (Sample 3) Exam 1 - Physics 202 - Patel SPRING 1998 FORM CODE - A (solution key at end of exam) Be sue to fill in you student numbe and FORM lette (A, B, C) on you answe sheet. If you foget to include

More information

Rotational Motion: Statics and Dynamics

Rotational Motion: Statics and Dynamics Physics 07 Lectue 17 Goals: Lectue 17 Chapte 1 Define cente of mass Analyze olling motion Intoduce and analyze toque Undestand the equilibium dynamics of an extended object in esponse to foces Employ consevation

More information

Physics 202, Lecture 2

Physics 202, Lecture 2 Physics 202, Lectue 2 Todays Topics Electic Foce and Electic Fields Electic Chages and Electic Foces Coulomb's Law Physical Field The Electic Field Electic Field Lines Motion of Chaged Paticle in Electic

More information

q r 1 4πε Review: Two ways to find V at any point in space: Integrate E dl: Sum or Integrate over charges: q 1 r 1 q 2 r 2 r 3 q 3

q r 1 4πε Review: Two ways to find V at any point in space: Integrate E dl: Sum or Integrate over charges: q 1 r 1 q 2 r 2 r 3 q 3 Review: Lectue : Consevation of negy and Potential Gadient Two ways to find V at any point in space: Integate dl: Sum o Integate ove chages: q q 3 P V = i 4πε q i i dq q 3 P V = 4πε dq ample of integating

More information

1 2 U CV. K dq I dt J nqv d J V IR P VI

1 2 U CV. K dq I dt J nqv d J V IR P VI o 5 o T C T F 9 T K T o C 7.5 L L T V VT Q mct nct Q F V ml F V dq A H k TH TC dt L pv nt Kt nt CV ideal monatomic gas 5 CV ideal diatomic gas w/o vibation V W pdv V U Q W W Q e Q Q e Canot H C T T S C

More information

Physics 1502: Lecture 4 Today s Agenda

Physics 1502: Lecture 4 Today s Agenda 1 Physics 1502: Today s genda nnouncements: Lectues posted on: www.phys.uconn.edu/~cote/ HW assignments, solutions etc. Homewok #1: On Mastephysics today: due next Fiday Go to masteingphysics.com and egiste

More information

An o5en- confusing point:

An o5en- confusing point: An o5en- confusing point: Recall this example fom last lectue: E due to a unifom spheical suface chage, density = σ. Let s calculate the pessue on the suface. Due to the epulsive foces, thee is an outwad

More information

Gauss s Law: Circuits

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

More information

Electric Charge and Field

Electric Charge and Field lectic Chage and ield Chapte 6 (Giancoli) All sections ecept 6.0 (Gauss s law) Compaison between the lectic and the Gavitational foces Both have long ange, The electic chage of an object plas the same

More information

Phys-272 Lecture 13. Magnetism Magnetic forces

Phys-272 Lecture 13. Magnetism Magnetic forces Phys-7 Lectue 13 Magnetism Magnetic foces Chaged paticle motion in a constant field - velocity in plane to. Suppose we have a magnetic field given by 0 and a paticle stats out at the oigin moving in the

More information

ELECTROSTATICS::BHSEC MCQ 1. A. B. C. D.

ELECTROSTATICS::BHSEC MCQ 1. A. B. C. D. ELETROSTATIS::BHSE 9-4 MQ. A moving electic chage poduces A. electic field only. B. magnetic field only.. both electic field and magnetic field. D. neithe of these two fields.. both electic field and magnetic

More information

Circular Motion & Torque Test Review. The period is the amount of time it takes for an object to travel around a circular path once.

Circular Motion & Torque Test Review. The period is the amount of time it takes for an object to travel around a circular path once. Honos Physics Fall, 2016 Cicula Motion & Toque Test Review Name: M. Leonad Instuctions: Complete the following woksheet. SHOW ALL OF YOUR WORK ON A SEPARATE SHEET OF PAPER. 1. Detemine whethe each statement

More information

Appendix B The Relativistic Transformation of Forces

Appendix B The Relativistic Transformation of Forces Appendix B The Relativistic Tansfomation of oces B. The ou-foce We intoduced the idea of foces in Chapte 3 whee we saw that the change in the fou-momentum pe unit time is given by the expession d d w x

More information

Look over Chapter 22 sections 1-8 Examples 2, 4, 5, Look over Chapter 16 sections 7-9 examples 6, 7, 8, 9. Things To Know 1/22/2008 PHYS 2212

Look over Chapter 22 sections 1-8 Examples 2, 4, 5, Look over Chapter 16 sections 7-9 examples 6, 7, 8, 9. Things To Know 1/22/2008 PHYS 2212 PHYS 1 Look ove Chapte sections 1-8 xamples, 4, 5, PHYS 111 Look ove Chapte 16 sections 7-9 examples 6, 7, 8, 9 Things To Know 1) What is an lectic field. ) How to calculate the electic field fo a point

More information

Objects usually are charged up through the transfer of electrons from one object to the other.

Objects usually are charged up through the transfer of electrons from one object to the other. 1 Pat 1: Electic Foce 1.1: Review of Vectos Review you vectos! You should know how to convet fom pola fom to component fom and vice vesa add and subtact vectos multiply vectos by scalas Find the esultant

More information

Eventually transatlantic signals! From Last Time. Electromagnetic Waves. The idea of electric fields. The electric field.

Eventually transatlantic signals! From Last Time. Electromagnetic Waves. The idea of electric fields. The electric field. Fom Last Time Electomagnetic waves Chages, cuent and foces: Coulomb s law. Acceleating chages poduce an electomagnetic wave The idea of the electic field. Today Electic fields, magnetic fields, and thei

More information

Electric Field, Potential Energy, & Voltage

Electric Field, Potential Energy, & Voltage Slide 1 / 66 lectic Field, Potential negy, & oltage Wok Slide 2 / 66 Q+ Q+ The foce changes as chages move towads each othe since the foce depends on the distance between the chages. s these two chages

More information

Continuous Charge Distributions: Electric Field and Electric Flux

Continuous Charge Distributions: Electric Field and Electric Flux 8/30/16 Quiz 2 8/25/16 A positive test chage qo is eleased fom est at a distance away fom a chage of Q and a distance 2 away fom a chage of 2Q. How will the test chage move immediately afte being eleased?

More information

PHYS 1444 Lecture #5

PHYS 1444 Lecture #5 Shot eview Chapte 24 PHYS 1444 Lectue #5 Tuesday June 19, 212 D. Andew Bandt Capacitos and Capacitance 1 Coulom s Law The Fomula QQ Q Q F 1 2 1 2 Fomula 2 2 F k A vecto quantity. Newtons Diection of electic

More information

SEE LAST PAGE FOR SOME POTENTIALLY USEFUL FORMULAE AND CONSTANTS

SEE LAST PAGE FOR SOME POTENTIALLY USEFUL FORMULAE AND CONSTANTS Cicle instucto: Moow o Yethiaj Name: MEMORIL UNIVERSITY OF NEWFOUNDLND DEPRTMENT OF PHYSICS ND PHYSICL OCENOGRPHY Final Eam Phsics 5 Winte 3:-5: pil, INSTRUCTIONS:. Do all SIX (6) questions in section

More information

PY208 Matter & Interactions Final Exam S2005

PY208 Matter & Interactions Final Exam S2005 PY Matte & Inteactions Final Exam S2005 Name (pint) Please cicle you lectue section below: 003 (Ramakishnan 11:20 AM) 004 (Clake 1:30 PM) 005 (Chabay 2:35 PM) When you tun in the test, including the fomula

More information

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

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

More information

Electric field generated by an electric dipole

Electric field generated by an electric dipole Electic field geneated by an electic dipole ( x) 2 (22-7) We will detemine the electic field E geneated by the electic dipole shown in the figue using the pinciple of supeposition. The positive chage geneates

More information

Chapter 28: Magnetic Field and Magnetic Force. Chapter 28: Magnetic Field and Magnetic Force. Chapter 28: Magnetic fields. Chapter 28: Magnetic fields

Chapter 28: Magnetic Field and Magnetic Force. Chapter 28: Magnetic Field and Magnetic Force. Chapter 28: Magnetic fields. Chapter 28: Magnetic fields Chapte 8: Magnetic fiels Histoically, people iscoe a stone (e 3 O 4 ) that attact pieces of ion these stone was calle magnets. two ba magnets can attact o epel epening on thei oientation this is ue to

More information

FI 2201 Electromagnetism

FI 2201 Electromagnetism FI 2201 Electomagnetism Alexande A. Iskanda, Ph.D. Physics of Magnetism and Photonics Reseach Goup Electodynamics ELETROMOTIVE FORE AND FARADAY S LAW 1 Ohm s Law To make a cuent flow, we have to push the

More information

Lecture 8 - Gauss s Law

Lecture 8 - Gauss s Law Lectue 8 - Gauss s Law A Puzzle... Example Calculate the potential enegy, pe ion, fo an infinite 1D ionic cystal with sepaation a; that is, a ow of equally spaced chages of magnitude e and altenating sign.

More information

Review: Electrostatics and Magnetostatics

Review: Electrostatics and Magnetostatics Review: Electostatics and Magnetostatics In the static egime, electomagnetic quantities do not vay as a function of time. We have two main cases: ELECTROSTATICS The electic chages do not change postion

More information

Physics 235 Chapter 5. Chapter 5 Gravitation

Physics 235 Chapter 5. Chapter 5 Gravitation Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus

More information

20-9 ELECTRIC FIELD LINES 20-9 ELECTRIC POTENTIAL. Answers to the Conceptual Questions. Chapter 20 Electricity 241

20-9 ELECTRIC FIELD LINES 20-9 ELECTRIC POTENTIAL. Answers to the Conceptual Questions. Chapter 20 Electricity 241 Chapte 0 Electicity 41 0-9 ELECTRIC IELD LINES Goals Illustate the concept of electic field lines. Content The electic field can be symbolized by lines of foce thoughout space. The electic field is stonge

More information

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

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

More information

Magnetic field due to a current loop.

Magnetic field due to a current loop. Example using spheical hamonics Sp 18 Magnetic field due to a cuent loop. A cicula loop of adius a caies cuent I. We place the oigin at the cente of the loop, with pola axis pependicula to the plane of

More information

18.1 Origin of Electricity 18.2 Charged Objects and Electric Force

18.1 Origin of Electricity 18.2 Charged Objects and Electric Force 1 18.1 Oigin of lecticity 18. Chaged Objects and lectic Foce Thee ae two kinds of electic chage: positive and negative. The SI unit of electic chage is the coulomb (C). The magnitude of the chage on an

More information