Your Comments. during the last couple lectures its been getting really noisy and hard to hear, especially for the last couple rows.

Size: px
Start display at page:

Download "Your Comments. during the last couple lectures its been getting really noisy and hard to hear, especially for the last couple rows."

Transcription

1 You Comments lease explain the ight hand ule when thee ae two wies and ou ae ting to find the diection of the foce I am getting confused with all these ight hand ules So do ou have an age-old advice fo Unofficial? Afte Tuesdas lectue I felt like I undestood the toque stuff, but as soon as I stated going though these checkpoint questions I felt like I was in Memento and hadnt taken a single polaoid on Tuesda Can ou explain mathematicall, o at least qualitativel, the deivation/intuition of the iot- Savat Law? I feel the pe-lectue pesented it in a "tust us that this is tue" fashion duing the last couple lectues its been getting eall nois and had to hea, especiall fo the last couple ows The eason thee is such a discepanc between checkpoint scoes and i>clicke scoes is that thee is no incentive to do well on checkpoints, so most people simpl click andom answes and submit them Not that I'm encouaging ou to give points fo accuac on checkpoints Is it oka to sa that the field poduced b a loop will be paallel (o anti paallel) to mu vecto of the loop cause mu and want to be aligned? Also if E-fields and -fields ae elated b Loent boosts, ae mu naught and epsilon naught elated? M oommate and I ae having a competition to see who can get on the boad moe, since I didn't just click though the pelectue like SOMEONE, I think I deseve a shoutout Electicit & Magnetism Lectue 14, Slide 1

2 Ae we going to have to constantl deive the iot-savat law fo infinite wies with cuent (much like how we constantl used Gauss's Law to find the E-field fo vaious sphees/clindes), o is the (μ_o*i)/(2π) equation something we will use staight off the bat? hsics 212 Lectue 14 Toda s Concept: iot-savat Law d 0I d s ˆ 2 4 Electicit & Magnetism Lectue 14, Slide 2

3 F Right Hand Rule Review 1 ANY CROSS RODUCT qv F d F IL ˆ 0I d s Diection of Magnetic Moment Finges: Cuent in Loop Thumb: Magnetic Moment 3 Diection of Magnetic Field fom Wie Finges: Magnetic Field Thumb: Cuent Electicit & Magnetism Lectue 14, Slide 3

4 What is it? Fundamental law fo detemining the diection and magnitude of the magnetic field due to an element of cuent iot-savat Law: d 0I ds ˆ 2 4 We can use this law to calculate the magnetic field poduced b ANY cuent distibution UT Eas analtic calculations ae possible onl fo a few distibutions: Axis of Cuent Loop Infinite Staight Wie lan fo Toda: Mainl use the esults of these calculations! GOOD NEWS: Remembe Gauss Law? Allowed us to calculate E fo smmetical chage distibutions NEXT TIME: Intoduce Ampee s Law Allows us to calculate fo smmetical cuent distibutions Electicit & Magnetism Lectue 14, Slide 4

5 Magnitude: fom Infinite Line of Cuent Integating 0I Tm/ A distance fom wie d 4 0I d s ˆ 2 gives esult Cuent I OUT Diection: Thumb: on I Finges: cul in diection of Electicit & Magnetism Lectue 14, Slide 5

6 Cuents + Chages A long staight wie is caing cuent fom left to ight Two identical chages ae moving with equal speed Compae the magnitude of the foce on chage a moving diectl to the ight, to the magnitude of the foce on chage b moving up and to the ight at the instant shown (ie same distance fom the wie) A) F a > F b ) F a F b C) F a < F b (a) F v (b) Foces ae in diffeent diections v F F qv F qvsinq Same q, v, and q (90) I Electicit & Magnetism Lectue 14, Slide 6

7 Adding Magnetic Fields Two long wies ca opposite cuent x What is the diection of the magnetic field above, and midwa between the two wies caing cuent at the point maked X? A) Left ) Right C) Up D) Down E) Zeo x Electicit & Magnetism Lectue 14, Slide 7

8 Foce etween Cuent-Caing Wies I towads d F 12 I 2 L F 12 I 2 L o 2d I 1 us Anothe I towads us F Conclusion: Cuents in same diection attact! I towads us d F Anothe I awa fom us Conclusion: Cuents in opposite diection epel! Electicit & Magnetism Lectue 14, Slide 8

9 Checkoint 1 X F What is the diection of the foce on wie 2 due to wie 1? A) Up ) Down C) Into Sceen D) Out of sceen E) Zeo 2 wies with same-diection cuents ae attacted What is the diection of the toque on wie 2 due to wie 1? A) Up ) Down C) Into Sceen D) Out of sceen E) Zeo Unifom foce at eve segment of wie No toque about an axis If two wies ae caing cuent, and we ae asked to detemine the diection of net toque on one wie (Checkpoint Question 1 at 3), how do we detemine the diection of the vecto?

10 Checkoint 3 What is the diection of the foce on wie 2 due to wie 1? A) Up ) Down C) Into Sceen D) Out of sceen E) Zeo WHY? DRAW ICTURE! Electicit & Magnetism Lectue 14, Slide 10

11 Conside Foce on Smmetic Segments I F out of sceen I F into sceen Net Foce is Zeo! Electicit & Magnetism Lectue 14, Slide 11

12 Checkoint 3b What is toque on wie 2, due to wie 1? Thee is a net foce on the ight side pointing into the sceen and a net foce on the left side pointing out of the sceen Using the ight hand ule, this means that the toque is pointing up What is the diection of the toque on wie 2 due to The wie wie 1? will t to align with wie 1 A) Up ) Down C) Into Sceen D) Out of sceen E) Zeo I I F out of sceen F into sceen Electicit & Magnetism Lectue 14, Slide 12

13 Foce on cuent loop nea wie AA loop of wie with cuent flowing in a counteclockwise diection is located to the ight of a long wie with cuent flowing up As shown below What is the diection of the net foce on the loop? A) Up ) Down C) Left D) Right E) Zeo 1 X X 2 F 1 F 2 ~ 1/R 1 > 2 F 1 > F 2 Electicit & Magnetism Lectue 14, Slide 13

14 F top + F bottom 0 Checkoint 2 A cuent caing loop of width a and length b is placed nea a cuent caing wie How does the net foce on the loop compae to the net foce on a single wie segment of length a caing the same amount of cuent placed at the same distance fom the wie? 1 X X 2 X 1 F 1 F 2 ~ 1/R 1 > 2 F1 F net A The foces A ae in opposite diections The net C foces ae the same C The net D foce on the loop is geate than the net foce on the wie segment D The net E foce on the loop is smalle than the net foce on the wie segment E Thee is no net foce on the loop Electicit & Magnetism Lectue 14, Slide 14

15 on axis fom Cuent Loop I Resulting Field Cuent in Wie Electicit & Magnetism Lectue 14, Slide 15

16 Two Cuent Loops Two identical loops ae hung next to each othe Cuent flows in the same diection in both The loops will: A) Attact each othe ) Repel each othe Two was to see this: 1) Like cuents attact 2) Look like ba magnets N S N S Electicit & Magnetism Lectue 14, Slide 17

17 Calculation Two paallel hoiontal wies ae located in the vetical (x,) plane as shown Each wie caies a cuent of I 1A flowing in the diections shown What is the field at point? I 1 1A x 3cm I 2 1A Font view Side view Conceptual Analsis Each wie ceates a magnetic field at fom infinite wie: m 0 I / 2p Total magnetic field at obtained fom supeposition Stategic Analsis Calculate at fom each wie sepaatel Total = vecto sum of individual fields Electicit & Magnetism Lectue 14, Slide 19

18 Calculation Two paallel hoiontal wies ae located in the vetical (x,) plane as shown Each wie caies a cuent of I 1A flowing in the diections shown What is the field at point? I 1 1A x 3cm I 2 1A Font view Side view What is the diection of at poduced b the top cuent I 1? A C D E Electicit & Magnetism Lectue 14, Slide 20

19 What is the diection of at poduced b the bottom cuent I 2? Calculation Two paallel hoiontal wies ae located in the vetical (x,) plane as shown Each wie caies a cuent of I 1A flowing in the diections shown What is the field at point? Font view I 1 1A I 2 1A x 3cm Side view A C D E Electicit & Magnetism Lectue 14, Slide 21

20 Calculation Two paallel hoiontal wies ae located in the vetical (x,) plane as shown Each wie caies a cuent of I 1A flowing in the diections shown What is the field at point? I 1 1A x 3cm I 2 1A What is the diection of at? Font view Side view 90 o A C D Electicit & Magnetism Lectue 14, Slide 22

21 Calculation Two paallel hoiontal wies ae located in the vetical (x,) plane as shown Each wie caies a cuent of I 1A flowing in the diections shown What is the field at point? What is the magnitude of at poduced b the top cuent I 1? ( 0 4 x 10 7 Tm/A) A) 40 x 10 6 T ) 50 x 10 6 T C) 67 x 10 6 T What is? distance fom wie axis to 0I I ỵ Font view 3cm I 1 1A I 2 1A x 3cm Side view cm Electicit & Magnetism Lectue 14, Slide 23

22 top 4 x 10 6 T What is the magnitude of at? Calculation Two paallel hoiontal wies ae located in the vetical (x,) plane as shown Each wie caies a cuent of I 1A flowing in the diections shown What is the field at point? Font view I 1 1A I 2 1A x 3cm ( 0 4 x 10-7 T m/a) A) 32 x 10 6 T ) 48 x 10 6 T C) 64 x 10 6 T D) 80 x 10 6 T ỵ q 5cm 3cm q q 1 q 2 1 x 1 cosq 2 x 2 cosq x cosq Electicit & Magnetism Lectue 14, Slide 24

Magnetism: a new force!

Magnetism: a new force! -1 Magnetism: a new foce! o fa, we'e leaned about two foces: gaity and the electic field foce. F E = E, FE = E Definition of E-field kq E-fields ae ceated by chages: E = 2 E-field exets a foce on othe

More information

Samples of conceptual and analytical/numerical questions from chap 21, C&J, 7E

Samples of conceptual and analytical/numerical questions from chap 21, C&J, 7E CHAPTER 1 Magnetism CONCEPTUAL QUESTIONS Cutnell & Johnson 7E 3. ssm A chaged paticle, passing though a cetain egion of space, has a velocity whose magnitude and diection emain constant, (a) If it is known

More information

Problems on Force Exerted by a Magnetic Fields from Ch 26 T&M

Problems on Force Exerted by a Magnetic Fields from Ch 26 T&M Poblems on oce Exeted by a Magnetic ields fom Ch 6 TM Poblem 6.7 A cuent-caying wie is bent into a semicicula loop of adius that lies in the xy plane. Thee is a unifom magnetic field B Bk pependicula to

More information

Forces & Magnetic Dipoles. r r τ = μ B r

Forces & Magnetic Dipoles. r r τ = μ B r Foces & Magnetic Dipoles x θ F θ F. = AI τ = U = Fist electic moto invented by Faaday, 1821 Wie with cuent flow (in cup of Hg) otates aound a a magnet Faaday s moto Wie with cuent otates aound a Pemanent

More information

Your Comments. did not understand any of this wtf. so over my head I have no idea what I am doing :(

Your Comments. did not understand any of this wtf. so over my head I have no idea what I am doing :( You Comments Llamas, and why it is so difficult to get someone to buy me one as a pet. All ask is that it beathes fie. have simple needs people. Seiously. p.s. this lectue was had. did not undestand any

More information

Chapter 30: Magnetic Fields Due to Currents

Chapter 30: Magnetic Fields Due to Currents d Chapte 3: Magnetic Field Due to Cuent A moving electic chage ceate a magnetic field. One of the moe pactical way of geneating a lage magnetic field (.1-1 T) i to ue a lage cuent flowing though a wie.

More information

AP-C Magnetism. AP-C Objectives (from College Board Learning Objectives for AP Physics)

AP-C Magnetism. AP-C Objectives (from College Board Learning Objectives for AP Physics) AP-C Magnetism AP-C (fom Coege oad Leaning fo AP Physics) 1. oces on moving chages in magnetic fieds a. Cacuate the magnitude and diection of the foce in tems of q, v, and, and expain why the magnetic

More information

Moment and couple. In 3-D, because the determination of the distance can be tedious, a vector approach becomes advantageous. r r

Moment and couple. In 3-D, because the determination of the distance can be tedious, a vector approach becomes advantageous. r r Moment and couple In 3-D, because the detemination of the distance can be tedious, a vecto appoach becomes advantageous. o k j i M k j i M o ) ( ) ( ) ( + + M o M + + + + M M + O A Moment about an abita

More information

Gauss Law in dielectrics

Gauss Law in dielectrics Gauss Law in dielectics We fist deive the diffeential fom of Gauss s law in the pesence of a dielectic. Recall, the diffeential fom of Gauss Law is This law is always tue. E In the pesence of dielectics,

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

Chapter F. Magnetism. Blinn College - Physics Terry Honan

Chapter F. Magnetism. Blinn College - Physics Terry Honan Chapte F Magnetism Blinn College - Physics 46 - Tey Honan F. - Magnetic Dipoles and Magnetic Fields Electomagnetic Duality Thee ae two types of "magnetic chage" o poles, Noth poles N and South poles S.

More information

Physics 202, Lecture 4. Gauss s Law: Review

Physics 202, Lecture 4. Gauss s Law: Review Physics 202, Lectue 4 Today s Topics Review: Gauss s Law Electic Potential (Ch. 25-Pat I) Electic Potential Enegy and Electic Potential Electic Potential and Electic Field Next Tuesday: Electic Potential

More information

Magnetic Field and Magnetic Forces. Young and Freedman Chapter 27

Magnetic Field and Magnetic Forces. Young and Freedman Chapter 27 Magnetic Field and Magnetic Foces Young and Feedman Chapte 27 Intoduction Reiew - electic fields 1) A chage (o collection of chages) poduces an electic field in the space aound it. 2) The electic field

More information

Chapter 26 - Electric Field. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University

Chapter 26 - Electric Field. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University Chapte 6 lectic Field A PowePoint Pesentation by Paul. Tippens, Pofesso of Physics Southen Polytechnic State Univesity 7 Objectives: Afte finishing this unit you should be able to: Define the electic field

More information

Problem Set 6: Solutions

Problem Set 6: Solutions UNIVESITY OF ALABAMA Depatment of Physics and Astonomy PH 16-4 / LeClai Fall 28 Poblem Set 6: Solutions 1. Seway 29.55 Potons having a kinetic enegy of 5. MeV ae moving in the positive x diection and ente

More information

Voltage ( = Electric Potential )

Voltage ( = Electric Potential ) V-1 of 9 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

Vector Calculus: Are you ready? Vectors in 2D and 3D Space: Review

Vector Calculus: Are you ready? Vectors in 2D and 3D Space: Review Vecto Calculus: Ae you eady? Vectos in D and 3D Space: Review Pupose: Make cetain that you can define, and use in context, vecto tems, concepts and fomulas listed below: Section 7.-7. find the vecto defined

More information

Physics 107 HOMEWORK ASSIGNMENT #14

Physics 107 HOMEWORK ASSIGNMENT #14 Physics 107 HOMEWORK ASSIGNMENT #14 Cutnell & Johnson, 7 th edition Chapte 17: Poblem 44, 60 Chapte 18: Poblems 14, 18, 8 **44 A tube, open at only one end, is cut into two shote (nonequal) lengths. The

More information

A couple is a pair of forces, equal in magnitude, oppositely directed, and displaced by perpendicular distance, d. F A F B (= -F A

A couple is a pair of forces, equal in magnitude, oppositely directed, and displaced by perpendicular distance, d. F A F B (= -F A 5 Moment of a Couple Ref: Hibbele 4.6, edfod & Fowle: Statics 4.4 couple is a pai of foces, equal in magnitude, oppositely diected, and displaced by pependicula distance, d. d (= - ) Since the foces ae

More information

AP Physics Electromagnetic Wrap Up

AP Physics Electromagnetic Wrap Up AP Physics Electomagnetic Wap Up Hee ae the gloious equations fo this wondeful section. F qsin This is the equation fo the magnetic foce acting on a moing chaged paticle in a magnetic field. The angle

More information

Chapter 13 Gravitation. Problems: 1, 4, 5, 7, 18, 19, 25, 29, 31, 33, 43

Chapter 13 Gravitation. Problems: 1, 4, 5, 7, 18, 19, 25, 29, 31, 33, 43 Chapte 13 Gavitation Poblems: 1, 4, 5, 7, 18, 19, 5, 9, 31, 33, 43 Evey object in the univese attacts evey othe object. This is called gavitation. We e use to dealing with falling bodies nea the Eath.

More information

Magnetism. The Magnetic Force. B x x x x x x x x x x x x v x x x x x x. F = q

Magnetism. The Magnetic Force. B x x x x x x x x x x x x v x x x x x x. F = q Magnetism The Magnetic Foce F = qe + qv x x x x x x x x x x x x v x x x x x x F q v q F v F = q 0 IM intoduced the fist had disk in 1957, when data usually was stoed on tapes. It consisted of 50 plattes,

More information

Voltage ( = Electric Potential )

Voltage ( = Electric Potential ) V-1 Voltage ( = Electic 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 is

More information

Poynting Vector and Energy Flow in a Capacitor Challenge Problem Solutions

Poynting Vector and Energy Flow in a Capacitor Challenge Problem Solutions Poynting Vecto an Enegy Flow in a Capacito Challenge Poblem Solutions Poblem 1: A paallel-plate capacito consists of two cicula plates, each with aius R, sepaate by a istance. A steay cuent I is flowing

More information

The force between electric charges. Comparing gravity and the interaction between charges. Coulomb s Law. Forces between two charges

The force between electric charges. Comparing gravity and the interaction between charges. Coulomb s Law. Forces between two charges The foce between electic chages Coulomb s Law Two chaged objects, of chage q and Q, sepaated by a distance, exet a foce on one anothe. The magnitude of this foce is given by: kqq Coulomb s Law: F whee

More information

Deflection of Electrons by Electric and Magnetic Fields

Deflection of Electrons by Electric and Magnetic Fields Physics 233 Expeiment 42 Deflection of Electons by Electic and Magnetic Fields Refeences Loain, P. and D.R. Coson, Electomagnetism, Pinciples and Applications, 2nd ed., W.H. Feeman, 199. Intoduction An

More information

XIIth PHYSICS (C2, G2, C, G) Solution

XIIth PHYSICS (C2, G2, C, G) Solution XIIth PHYSICS (C, G, C, G) -6- Solution. A 5 W, 0 V bulb and a 00 W, 0 V bulb ae connected in paallel acoss a 0 V line nly 00 watt bulb will fuse nly 5 watt bulb will fuse Both bulbs will fuse None of

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

F = kq 1q 2 r 2. F 13 = k( q)(2q) 2a 2 cosθˆx + sinθŷ F 14 = k( 2q)(2q) F 12 = k(q)(2q) a 2. tanθ = a a

F = kq 1q 2 r 2. F 13 = k( q)(2q) 2a 2 cosθˆx + sinθŷ F 14 = k( 2q)(2q) F 12 = k(q)(2q) a 2. tanθ = a a .1 What ae the hoizontal and vetical components of the esultant electostatic foce on the chage in the lowe left cone of the squae if q =1. 1 7 and a =5.cm? +q -q a +q a -q F = kq 1q F 1 = k(q)(q) a F 13

More information

12. Rolling, Torque, and Angular Momentum

12. Rolling, Torque, and Angular Momentum 12. olling, Toque, and Angula Momentum 1 olling Motion: A motion that is a combination of otational and tanslational motion, e.g. a wheel olling down the oad. Will only conside olling with out slipping.

More information

General Physics (PHY 2130)

General Physics (PHY 2130) Geneal Physics (PHY 130) Lectue 11 Rotational kinematics and unifom cicula motion Angula displacement Angula speed and acceleation http://www.physics.wayne.edu/~apetov/phy130/ Lightning Review Last lectue:

More information

Lesson 8 Ampère s Law and Differential Operators

Lesson 8 Ampère s Law and Differential Operators Lesson 8 Ampèe s Law and Diffeential Opeatos Lawence Rees 7 You ma make a single cop of this document fo pesonal use without witten pemission 8 Intoduction Thee ae significant diffeences between the electic

More information

Solution Derivations for Capa #8

Solution Derivations for Capa #8 Solution Deivations fo Capa #8 1) A ass spectoete applies a voltage of 2.00 kv to acceleate a singly chaged ion (+e). A 0.400 T field then bends the ion into a cicula path of adius 0.305. What is the ass

More information

So we ll start with Angular Measure. Consider a particle moving in a circular path. (p. 220, Figure 7.1)

So we ll start with Angular Measure. Consider a particle moving in a circular path. (p. 220, Figure 7.1) Lectue 17 Cicula Motion (Chapte 7) Angula Measue Angula Speed and Velocity Angula Acceleation We ve aleady dealt with cicula motion somewhat. Recall we leaned about centipetal acceleation: when you swing

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

PY1052 Problem Set 8 Autumn 2004 Solutions

PY1052 Problem Set 8 Autumn 2004 Solutions PY052 Poblem Set 8 Autumn 2004 Solutions H h () A solid ball stats fom est at the uppe end of the tack shown and olls without slipping until it olls off the ight-hand end. If H 6.0 m and h 2.0 m, what

More information

Lab 5: Circular Motion

Lab 5: Circular Motion Lab 5: Cicula motion Physics 193 Fall 2006 Lab 5: Cicula Motion I. Intoduction The lab today involves the analysis of objects that ae moving in a cicle. Newton s second law as applied to cicula motion

More information

2008 Quarter-Final Exam Solutions

2008 Quarter-Final Exam Solutions 2008 Quate-final Exam - Solutions 1 2008 Quate-Final Exam Solutions 1 A chaged paticle with chage q and mass m stats with an initial kinetic enegy K at the middle of a unifomly chaged spheical egion of

More information

EXPERIMENT 16 THE MAGNETIC MOMENT OF A BAR MAGNET AND THE HORIZONTAL COMPONENT OF THE EARTH S MAGNETIC FIELD

EXPERIMENT 16 THE MAGNETIC MOMENT OF A BAR MAGNET AND THE HORIZONTAL COMPONENT OF THE EARTH S MAGNETIC FIELD 260 16-1. THEORY EXPERMENT 16 THE MAGNETC MOMENT OF A BAR MAGNET AND THE HORZONTAL COMPONENT OF THE EARTH S MAGNETC FELD The uose of this exeiment is to measue the magnetic moment μ of a ba magnet and

More information

Chapter 22. Outside a uniformly charged sphere, the field looks like that of a point charge at the center of the sphere.

Chapter 22. Outside a uniformly charged sphere, the field looks like that of a point charge at the center of the sphere. Chapte.3 What is the magnitude of a point chage whose electic field 5 cm away has the magnitude of.n/c. E E 5.56 1 11 C.5 An atom of plutonium-39 has a nuclea adius of 6.64 fm and atomic numbe Z94. Assuming

More information

MAGNETIC FIELDS AND FORCES 24

MAGNETIC FIELDS AND FORCES 24 MAGNETIC FIELDS AND FORCES 24 Q24.1. Reason: When a ba magnet is bought nea the cente of anothe ba magnet as shown in Figue Q24.1, the foce between the ba magnets is zeo. The attactive foce between the

More information

Exam 3: Equation Summary

Exam 3: Equation Summary MASSACHUSETTS INSTITUTE OF TECHNOLOGY Depatment of Physics Physics 8.1 TEAL Fall Tem 4 Momentum: p = mv, F t = p, Fext ave t= t f t= Exam 3: Equation Summay total = Impulse: I F( t ) = p Toque: τ = S S,P

More information

rotation -- Conservation of mechanical energy for rotation -- Angular momentum -- Conservation of angular momentum

rotation -- Conservation of mechanical energy for rotation -- Angular momentum -- Conservation of angular momentum Final Exam Duing class (1-3:55 pm) on 6/7, Mon Room: 41 FMH (classoom) Bing scientific calculatos No smat phone calculatos l ae allowed. Exam coves eveything leaned in this couse. Review session: Thusday

More information

Chapter 23: Gauss s Law

Chapter 23: Gauss s Law Chapte 3: Gauss s Law Homewok: Read Chapte 3 Questions, 5, 1 Poblems 1, 5, 3 Gauss s Law Gauss s Law is the fist of the fou Maxwell Equations which summaize all of electomagnetic theoy. Gauss s Law gives

More information

Mechanics 1: Motion in a Central Force Field

Mechanics 1: Motion in a Central Force Field Mechanics : Motion in a Cental Foce Field We now stud the popeties of a paticle of (constant) ass oving in a paticula tpe of foce field, a cental foce field. Cental foces ae ve ipotant in phsics and engineeing.

More information

Mon., 3/9 Tues., 3/10 Wed., 3/11 Thurs., 3/12 Fri., 3/ 13. RE19 HW19:RQ.42, 49, 52; P.61, 66, 69 RE20, Exp new RE ,3-4 Magnetic Force

Mon., 3/9 Tues., 3/10 Wed., 3/11 Thurs., 3/12 Fri., 3/ 13. RE19 HW19:RQ.42, 49, 52; P.61, 66, 69 RE20, Exp new RE ,3-4 Magnetic Force Mon., 3/9 Tues., 3/10 Wed., 3/11 Thus., 3/12 Fi., 3/ 13 Mon., 3/16 Tues., 3/17 Wed., 3/18 Thus., 3/19 Fi., 3/20 20.1,3-4 Magnetic Foce 20.2,5 Cuent and Motional Emf Quiz Ch 19, Lab 8 Cycloton & Electon

More information

The Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = -W/q 0 1V [Volt] =1 Nm/C

The Electric Potential, Electric Potential Energy and Energy Conservation. V = U/q 0. V = U/q 0 = -W/q 0 1V [Volt] =1 Nm/C Geneal Physics - PH Winte 6 Bjoen Seipel The Electic Potential, Electic Potential Enegy and Enegy Consevation Electic Potential Enegy U is the enegy of a chaged object in an extenal electic field (Unit

More information

Hour Exam No.1. p 1 v. p = e 0 + v^b. Note that the probe is moving in the direction of the unit vector ^b so the velocity vector is just ~v = v^b and

Hour Exam No.1. p 1 v. p = e 0 + v^b. Note that the probe is moving in the direction of the unit vector ^b so the velocity vector is just ~v = v^b and Hou Exam No. Please attempt all of the following poblems befoe the due date. All poblems count the same even though some ae moe complex than othes. Assume that c units ae used thoughout. Poblem A photon

More information

TALLINN UNIVERSITY OF TECHNOLOGY, INSTITUTE OF PHYSICS 14. NEWTON'S RINGS

TALLINN UNIVERSITY OF TECHNOLOGY, INSTITUTE OF PHYSICS 14. NEWTON'S RINGS 4. NEWTON'S RINGS. Obective Detemining adius of cuvatue of a long focal length plano-convex lens (lage adius of cuvatue).. Equipment needed Measuing micoscope, plano-convex long focal length lens, monochomatic

More information

Revision Guide for Chapter 11

Revision Guide for Chapter 11 Revision Guide fo Chapte 11 Contents Student s Checklist Revision Notes Momentum... 4 Newton's laws of motion... 4 Gavitational field... 5 Gavitational potential... 6 Motion in a cicle... 7 Summay Diagams

More information

Coordinate Systems L. M. Kalnins, March 2009

Coordinate Systems L. M. Kalnins, March 2009 Coodinate Sstems L. M. Kalnins, Mach 2009 Pupose of a Coodinate Sstem The pupose of a coodinate sstem is to uniquel detemine the position of an object o data point in space. B space we ma liteall mean

More information

Lecture 3 1/16. Torque on a Dipole. The magnitude of the torque: center of mass. Fsin F -Q. dipole moment. torque points into the page

Lecture 3 1/16. Torque on a Dipole. The magnitude of the torque: center of mass. Fsin F -Q. dipole moment. torque points into the page Lectue 3 /6 Toque on Dipole F F sin The mgnitude of the toque: Fsin d Fsin psin p ( d Fsin d qsin F - d F θ cente of mss dipole moment p q d toque points into the pge Lectue 3 /6 uiz uestion An electic

More information

Multiple choice questions [70 points]

Multiple choice questions [70 points] Multiple choice questions [70 points] Answe all of the following questions. Read each question caefull. Fill the coect bubble on ou scanton sheet. Each question has exactl one coect answe. All questions

More information

PY1052 Problem Set 3 Autumn 2004 Solutions

PY1052 Problem Set 3 Autumn 2004 Solutions PY1052 Poblem Set 3 Autumn 2004 Solutions C F = 8 N F = 25 N 1 2 A A (1) A foce F 1 = 8 N is exeted hoizontally on block A, which has a mass of 4.5 kg. The coefficient of static fiction between A and the

More information

The Role of Gravity in Orbital Motion

The Role of Gravity in Orbital Motion ! The Role of Gavity in Obital Motion Pat of: Inquiy Science with Datmouth Developed by: Chistophe Caoll, Depatment of Physics & Astonomy, Datmouth College Adapted fom: How Gavity Affects Obits (Ohio State

More information

Chapter 13 Gravitation

Chapter 13 Gravitation Chapte 13 Gavitation Newton, who extended the concept of inetia to all bodies, ealized that the moon is acceleating and is theefoe subject to a centipetal foce. He guessed that the foce that keeps the

More information

Trigonometric Functions of Any Angle

Trigonometric Functions of Any Angle Tigonomet Module T2 Tigonometic Functions of An Angle Copight This publication The Nothen Albeta Institute of Technolog 2002. All Rights Reseved. LAST REVISED Decembe, 2008 Tigonometic Functions of An

More information

Experiment 6: Centripetal Force

Experiment 6: Centripetal Force Name Section Date Intoduction Expeiment 6: Centipetal oce This expeiment is concened with the foce necessay to keep an object moving in a constant cicula path. Accoding to Newton s fist law of motion thee

More information

Modern Linear Algebra

Modern Linear Algebra Hochschule fü Witschaft und Recht Belin Belin School of Economics and Law Wintesemeste 04/05 D. Hon Mathematics fo Business and Economics LV-N. 0069.0 Moden Linea Algeba (A Geometic Algeba cash couse,

More information

PHYSICS 111 HOMEWORK SOLUTION #5. March 3, 2013

PHYSICS 111 HOMEWORK SOLUTION #5. March 3, 2013 PHYSICS 111 HOMEWORK SOLUTION #5 Mach 3, 2013 0.1 You 3.80-kg physics book is placed next to you on the hoizontal seat of you ca. The coefficient of static fiction between the book and the seat is 0.650,

More information

Learning Objectives. Decreasing size. ~10 3 m. ~10 6 m. ~10 10 m 1/22/2013. Describe ionic, covalent, and metallic, hydrogen, and van der Waals bonds.

Learning Objectives. Decreasing size. ~10 3 m. ~10 6 m. ~10 10 m 1/22/2013. Describe ionic, covalent, and metallic, hydrogen, and van der Waals bonds. Lectue #0 Chapte Atomic Bonding Leaning Objectives Descibe ionic, covalent, and metallic, hydogen, and van de Waals bonds. Which mateials exhibit each of these bonding types? What is coulombic foce of

More information

Lesson 9 Dipoles and Magnets

Lesson 9 Dipoles and Magnets Lesson 9 Dipoles and Magnets Lawence B. Rees 007. You may make a single copy of this document fo pesonal use without witten pemission. 9.0 Intoduction In this chapte we will lean about an assotment of

More information

Unit Vectors. the unit vector rˆ. Thus, in the case at hand, 5.00 rˆ, means 5.00 m/s at 36.0.

Unit Vectors. the unit vector rˆ. Thus, in the case at hand, 5.00 rˆ, means 5.00 m/s at 36.0. Unit Vectos What is pobabl the most common mistake involving unit vectos is simpl leaving thei hats off. While leaving the hat off a unit vecto is a nast communication eo in its own ight, it also leads

More information

Physics 111 Fall 2007 Electrostatic Forces and the Electric Field - Solutions

Physics 111 Fall 2007 Electrostatic Forces and the Electric Field - Solutions Physics 111 Fall 007 Electostatic Foces an the Electic Fiel - Solutions 1. Two point chages, 5 µc an -8 µc ae 1. m apat. Whee shoul a thi chage, equal to 5 µc, be place to make the electic fiel at the

More information

Chapter 22 The Electric Field II: Continuous Charge Distributions

Chapter 22 The Electric Field II: Continuous Charge Distributions Chapte The lectic Field II: Continuous Chage Distibutions 1 [M] A unifom line chage that has a linea chage density l equal to.5 nc/m is on the x axis between x and x 5. m. (a) What is its total chage?

More information

The Grating Spectrometer and Atomic Spectra

The Grating Spectrometer and Atomic Spectra PHY 19 Gating Spectomete 1 The Gating Spectomete and Atomic Specta Intoduction In the pevious expeiment diffaction and intefeence wee discussed and at the end a diffaction gating was intoduced. In this

More information

Review Module: Dot Product

Review Module: Dot Product MASSACHUSETTS INSTITUTE OF TECHNOLOGY Depatment of Physics 801 Fall 2009 Review Module: Dot Poduct We shall intoduce a vecto opeation, called the dot poduct o scala poduct that takes any two vectos and

More information

Copyright 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Copyright 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapte 5. Foce and Motion In this chapte we study causes of motion: Why does the windsufe blast acoss the wate in the way he does? The combined foces of the wind, wate, and gavity acceleate him accoding

More information

9. Mathematics Practice Paper for Class XII (CBSE) Available Online Tutoring for students of classes 4 to 12 in Physics, Chemistry, Mathematics

9. Mathematics Practice Paper for Class XII (CBSE) Available Online Tutoring for students of classes 4 to 12 in Physics, Chemistry, Mathematics Available Online Tutoing fo students of classes 4 to 1 in Physics, 9. Mathematics Class 1 Pactice Pape 1 3 1. Wite the pincipal value of cos.. Wite the ange of the pincipal banch of sec 1 defined on the

More information

Physics: Electromagnetism Spring PROBLEM SET 6 Solutions

Physics: Electromagnetism Spring PROBLEM SET 6 Solutions Physics: Electomagnetism Sping 7 Physics: Electomagnetism Sping 7 PROBEM SET 6 Solutions Electostatic Enegy Basics: Wolfson and Pasachoff h 6 Poblem 7 p 679 Thee ae si diffeent pais of equal chages and

More information

Mechanics 1: Work, Power and Kinetic Energy

Mechanics 1: Work, Power and Kinetic Energy Mechanics 1: Wok, Powe and Kinetic Eneg We fist intoduce the ideas of wok and powe. The notion of wok can be viewed as the bidge between Newton s second law, and eneg (which we have et to define and discuss).

More information

Episode 401: Newton s law of universal gravitation

Episode 401: Newton s law of universal gravitation Episode 401: Newton s law of univesal gavitation This episode intoduces Newton s law of univesal gavitation fo point masses, and fo spheical masses, and gets students pactising calculations of the foce

More information

Chapter 2. Electrostatics

Chapter 2. Electrostatics Chapte. Electostatics.. The Electostatic Field To calculate the foce exeted by some electic chages,,, 3,... (the souce chages) on anothe chage Q (the test chage) we can use the pinciple of supeposition.

More information

Internal Resistance of cell & Combinations of Cells By R. S. Saini. (M.Sc. Physics, M.Ed.) Kendriya Vidyalaya, Sector 47, Chandigarh

Internal Resistance of cell & Combinations of Cells By R. S. Saini. (M.Sc. Physics, M.Ed.) Kendriya Vidyalaya, Sector 47, Chandigarh ntenal Resistance of cell & Combinations of Cells 01.06.09 By R. S. Saini (M.Sc. Physics, M.d.) Kendiya idyalaya, Secto 47, Chandigah 9417071540 Souces of emf: The electo motive foce is the maximum potential

More information

Skills Needed for Success in Calculus 1

Skills Needed for Success in Calculus 1 Skills Needed fo Success in Calculus Thee is much appehension fom students taking Calculus. It seems that fo man people, "Calculus" is snonmous with "difficult." Howeve, an teache of Calculus will tell

More information

Experiment MF Magnetic Force

Experiment MF Magnetic Force Expeiment MF Magnetic Foce Intoduction The magnetic foce on a cuent-caying conducto is basic to evey electic moto -- tuning the hands of electic watches and clocks, tanspoting tape in Walkmans, stating

More information

8-1 Newton s Law of Universal Gravitation

8-1 Newton s Law of Universal Gravitation 8-1 Newton s Law of Univesal Gavitation One of the most famous stoies of all time is the stoy of Isaac Newton sitting unde an apple tee and being hit on the head by a falling apple. It was this event,

More information

Insight: If the angular speed of the fan blade were to double to 24 rad/s, the kinetic energy would quadruple to 16 J.

Insight: If the angular speed of the fan blade were to double to 24 rad/s, the kinetic energy would quadruple to 16 J. HOMEWORK Capte 0 57. Pictue te Poblem e an blade otates about its ais wit a constant angula speed. Stateg Use equation 0-7 o te kinetic eneg o a otating object to solve o te moment o inetia. Solution Solve

More information

UNIT 21: ELECTRICAL AND GRAVITATIONAL POTENTIAL Approximate time two 100-minute sessions

UNIT 21: ELECTRICAL AND GRAVITATIONAL POTENTIAL Approximate time two 100-minute sessions Name St.No. - Date(YY/MM/DD) / / Section Goup# UNIT 21: ELECTRICAL AND GRAVITATIONAL POTENTIAL Appoximate time two 100-minute sessions OBJECTIVES I began to think of gavity extending to the ob of the moon,

More information

Lesson 7 Gauss s Law and Electric Fields

Lesson 7 Gauss s Law and Electric Fields Lesson 7 Gauss s Law and Electic Fields Lawence B. Rees 7. You may make a single copy of this document fo pesonal use without witten pemission. 7. Intoduction While it is impotant to gain a solid conceptual

More information

UNIT CIRCLE TRIGONOMETRY

UNIT CIRCLE TRIGONOMETRY UNIT CIRCLE TRIGONOMETRY The Unit Cicle is the cicle centeed at the oigin with adius unit (hence, the unit cicle. The equation of this cicle is + =. A diagam of the unit cicle is shown below: + = - - -

More information

Chapter 3: Vectors and Coordinate Systems

Chapter 3: Vectors and Coordinate Systems Coodinate Systems Chapte 3: Vectos and Coodinate Systems Used to descibe the position of a point in space Coodinate system consists of a fied efeence point called the oigin specific aes with scales and

More information

A r. (Can you see that this just gives the formula we had above?)

A r. (Can you see that this just gives the formula we had above?) 24-1 (SJP, Phys 1120) lectic flux, and Gauss' law Finding the lectic field due to a bunch of chages is KY! Once you know, you know the foce on any chage you put down - you can pedict (o contol) motion

More information

Gauss s Law. Figure 22.1 A great white shark can detect tiny electric fields generated by its prey.

Gauss s Law. Figure 22.1 A great white shark can detect tiny electric fields generated by its prey. lectic Fields and Gauss s Law What We Will Lean 711.1 Definition of an lectic Field 711. Field Lines 71 Point Chage 71 Two Point Chages of Opposite Sign 71 Two Point Chages with the Same Sign 71 Geneal

More information

MAGNETIC FIELD AROUND CURRENT-CARRYING WIRES. point in space due to the current in a small segment ds. a for field around long wire

MAGNETIC FIELD AROUND CURRENT-CARRYING WIRES. point in space due to the current in a small segment ds. a for field around long wire MAGNETC FELD AROUND CURRENT-CARRYNG WRES How will we tckle this? Pln: 1 st : Will look t contibution d to the totl mgnetic field t some point in spce due to the cuent in smll segment of wie iot-svt Lw

More information

Review of Vectors. Appendix A A.1 DESCRIBING THE 3D WORLD: VECTORS. 3D Coordinates. Basic Properties of Vectors: Magnitude and Direction.

Review of Vectors. Appendix A A.1 DESCRIBING THE 3D WORLD: VECTORS. 3D Coordinates. Basic Properties of Vectors: Magnitude and Direction. Appendi A Review of Vectos This appendi is a summa of the mathematical aspects of vectos used in electicit and magnetism. Fo a moe detailed intoduction to vectos, see Chapte 1. A.1 DESCRIBING THE 3D WORLD:

More information

On Correlation Coefficient. The correlation coefficient indicates the degree of linear dependence of two random variables.

On Correlation Coefficient. The correlation coefficient indicates the degree of linear dependence of two random variables. C.Candan EE3/53-METU On Coelation Coefficient The coelation coefficient indicates the degee of linea dependence of two andom vaiables. It is defined as ( )( )} σ σ Popeties: 1. 1. (See appendi fo the poof

More information

Multiple choice questions [60 points]

Multiple choice questions [60 points] 1 Multiple choice questions [60 points] Answe all o the ollowing questions. Read each question caeully. Fill the coect bubble on you scanton sheet. Each question has exactly one coect answe. All questions

More information

CHAPTER 17 MAGNETIC DIPOLE MOMENT

CHAPTER 17 MAGNETIC DIPOLE MOMENT 1 CHAPTER 17 MAGNETIC DIPOLE MOMENT 17.1 Intoduction A numbe of diffeent units fo expessing magnetic dipole moment (heeafte simply magnetic moment ) ae commonly seen in the liteatue, including, fo example,

More information

GRAVITATIONAL FIELD: CHAPTER 11. The groundwork for Newton s great contribution to understanding gravity was laid by three majors players:

GRAVITATIONAL FIELD: CHAPTER 11. The groundwork for Newton s great contribution to understanding gravity was laid by three majors players: CHAPT 11 TH GAVITATIONAL FILD (GAVITY) GAVITATIONAL FILD: The goundwok fo Newton s geat contibution to undestanding gavity was laid by thee majos playes: Newton s Law of Gavitation o gavitational and inetial

More information

Chapter 5 Review - Part I

Chapter 5 Review - Part I Math 17 Chate Review Pat I Page 1 Chate Review - Pat I I. Tyes of Polynomials A. Basic Definitions 1. In the tem b m, b is called the coefficient, is called the vaiable, and m is called the eonent on the

More information

Chapter 19: Electric Charges, Forces, and Fields ( ) ( 6 )( 6

Chapter 19: Electric Charges, Forces, and Fields ( ) ( 6 )( 6 Chapte 9 lectic Chages, Foces, an Fiels 6 9. One in a million (0 ) ogen molecules in a containe has lost an electon. We assume that the lost electons have been emove fom the gas altogethe. Fin the numbe

More information

Introduction to Electric Potential

Introduction to Electric Potential Univesiti Teknologi MARA Fakulti Sains Gunaan Intoduction to Electic Potential : A Physical Science Activity Name: HP: Lab # 3: The goal of today s activity is fo you to exploe and descibe the electic

More information

Uniform Rectilinear Motion

Uniform Rectilinear Motion Engineeing Mechanics : Dynamics Unifom Rectilinea Motion Fo paticle in unifom ectilinea motion, the acceleation is zeo and the elocity is constant. d d t constant t t 11-1 Engineeing Mechanics : Dynamics

More information

Transformations in Homogeneous Coordinates

Transformations in Homogeneous Coordinates Tansfomations in Homogeneous Coodinates (Com S 4/ Notes) Yan-Bin Jia Aug, 6 Homogeneous Tansfomations A pojective tansfomation of the pojective plane is a mapping L : P P defined as u a b c u au + bv +

More information

FXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it.

FXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it. Candidates should be able to : Descibe how a mass ceates a gavitational field in the space aound it. Define gavitational field stength as foce pe unit mass. Define and use the peiod of an object descibing

More information

Gravitation. AP Physics C

Gravitation. AP Physics C Gavitation AP Physics C Newton s Law of Gavitation What causes YOU to be pulled down? THE EARTH.o moe specifically the EARTH S MASS. Anything that has MASS has a gavitational pull towads it. F α Mm g What

More information

Introduction to Fluid Mechanics

Introduction to Fluid Mechanics Chapte 1 1 1.6. Solved Examples Example 1.1 Dimensions and Units A body weighs 1 Ibf when exposed to a standad eath gavity g = 3.174 ft/s. (a) What is its mass in kg? (b) What will the weight of this body

More information

TRIGONOMETRY REVIEW. The Cosines and Sines of the Standard Angles

TRIGONOMETRY REVIEW. The Cosines and Sines of the Standard Angles TRIGONOMETRY REVIEW The Cosines and Sines of the Standad Angles P θ = ( cos θ, sin θ ) . ANGLES AND THEIR MEASURE In ode to define the tigonometic functions so that they can be used not only fo tiangula

More information

Displacement, Velocity And Acceleration

Displacement, Velocity And Acceleration Displacement, Velocity And Acceleation Vectos and Scalas Position Vectos Displacement Speed and Velocity Acceleation Complete Motion Diagams Outline Scala vs. Vecto Scalas vs. vectos Scala : a eal numbe,

More information