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


 Delphia Charles
 2 years ago
 Views:
Transcription
1 Chapte.3 What is the magnitude of a point chage whose electic field 5 cm away has the magnitude of.n/c. E E C.5 An atom of plutonium39 has a nuclea adius of 6.64 fm and atomic numbe Z94. Assuming that the positive chage is distibuted unifomly within the nucleus, what ae the magnitude and diection of the electic field at the suface of the nucleus due to the positive chage. Outside a unifomly chaged sphee, the field looks like that of a point chage at the cente of the sphee. E C ( m) N / C!.8 In Fig. 31, paticle 1 of chage 1 5 and paticle of chage + ae fixed to an xaxis (a) As a multiple of distance L, at what coodinate on the axis is the net electic field of the paticles zeo? (a) Sketch the net electic field lines. E1 E 1 (x,)
2 E 1 E 1 x E E 1 5 x (x L) 5 x (x L) 5 x (x L) x 1 (5 + 1)L 3.11 Figue 34 shows two chaged paticles on an x axis: C at x 3.m and C at x +3.m. What ae the (a) magnitude and (b) diection (elative to the positive diection of the x axis) of the net electic field poduced at point P at y +4.m x (., 4.) (3.,.) (+3.,.) We can do this poblem most easily by using the full vecto fom fo the electic field due to a point chage. ( 3.) i ˆ + (4. ) ˆ j m ˆ + + 3ˆ i + 4 ˆ j 5 ( (3))ˆ i + (4 ) ˆ j ˆ (3) + 4 5m 3ˆ i + 4 ˆ j 5
3 E E + + E C 4 π ε (5m) 3 ˆ 5 i + 4 ˆ j C 4 π ε (5m) 6 i ˆ + ˆ j N / C ˆ i C 4 π ε (5m) 3 ˆ i + 4 ˆ j 5.13 In Fig. 36, thee paticles ae fixed in place and have chages 1 +e and 3 +e. Distance a 6.µm. What ae the (a)magnitude and (b) diection of the net electic field at point P due to the paticles. 1 E E 3 E 1 3 The fields due to chages 1 and cancel exactly. This leaves us only to calculate the field due to 3. 1 a + a a E N / C at 45 a /.19. Find the magnitude and diection of the electic field at point P due to the electic dipole. You may assume that >>d
4 (,d/ ) + (, )  (,d/ ) We begin by witing the exact field. ( ) i ˆ + ( d ) ˆ j ( ) i ˆ + ( ( d )) ˆ j + ( d ) + ( d ) E E + + E ˆ + ˆ ˆ + + i ˆ d ˆ j + ( d ) ˆ i ˆ + d ˆ j + ( d ) We can substitute in. In the last step, since d/ is vey small we ignoe this tem. emembe that the diection of p is in the +j diection in this poblem (fom  to + chage).
5 E E + + E ˆ + ˆ ( + ( d ) ) i ˆ d ˆ j + ( d ) ( + ( d ) ) i ˆ + d ˆ j + ( d ) ( indicates downwad) d ( + ( d ˆ j ) ) 3/ p 3 (1 + ( d ˆ j ) ) 3/ p 3.4 In Fig 44, a thin glass od foms a semicicle of adius 5.cm. Chage is unifomly distibuted along the od, with pc in the uppe half and 4.5 pc in the l lowe half. What ae the (a) magnitude and (b) diection elative to the positive diection of the x axis of the electic field E a P, the cente of the cicle. Because of the symmety in the poblem, we can see that the net field will point downwad. We also can see that the contibution fom the bottom uate cicle is eual to the contibution fom the top uate cicle. Because of this, we only need to compute the downwad component due to the top uate cicle and multiply by. d d E We begin by defining a chage pe unit length π /
6 We now find the component of inteest and integate... d de cosθ de d d dθ The last facto of is because thee ae two uate ings. π / π / d dθ cosθ π / π 8ε tot 4ε cosθ dθ.5 In Fig 45, two cuved plastic ods, one of chage + and one of chage , fo a cicle of adius in the XY plane.. Te x axis passes though thei connection points and the chage is distibuted unifomly on both ods. What ae the magnitude and diection of the electic field E poduces at P, the cente of the cicle. Because of the symmety in the poblem, we can see that the net field will point downwad. We also can see that the contibution fom the bottom half cicle is eual to the contibution fom the top half cicle. Because of this, we only need to compute the downwad component due to the top half cicle and multiply by. d θ θ de We begin by defining a chage pe unit length
7 π We now find the component of inteest and integate... The last facto of is because thee ae two half ings. d de cosθ de d d dθ π / π / π / π / d dθ cosθ πε tot π / π / πε cosθ dθ.6
8 i de dez i z { Because of the symmety, we only need to compute the field along the axis (called z). de z de cosθ de d + z d 1 dϕ cosθ z + z E z E z π π π de z 1 dϕ ( + z ) 1 z dϕ ( + z ) 3/ 1 z ε ( + z ) 3/ z + z Now that we know the field, we take the deivative with espect to z and set it eual to zeo to find the location of the maximum field. m E z 1z f ( + z ) 3/ de z dz m 1(  z ) f ( + z ) 5/ z 1
9 3. In Fig. 51, positive chage 7.81pC is spead unifomly along a thin nonconducting od of length L 14.5cm. What ae the (a) magnitude and (b) diection (elative to the x axis of the electic field poduced at a distance 6.cm fom the od along its pependicula bisecto. (,d) L / L / Fist we wite d fo a little length of chage We then wite the,, ˆ fo the chage d. d dx ( x) + (d ) ( x) i ˆ + (d ) ˆ j ˆ x i ˆ + d ˆ j x + d We can then compute the x and y components of the Electic Field. You may need dx x (a + x ) 3/ a a + x
10 E E x d ˆ d dx d (x + d ) 3/ dx x i ˆ + d ˆ j (x + d ) x + d d L / d + L / 4 L / d + L / 4 d L d + L / 4 πε d L 4d + L dx d (x + d ) 3/ d x d + x L / L / Now we can compute with numbes C C / m.145m d.6m C / m πε.6m.145m 4(.6m) + (.145m) 1.43N / C.33 In Fig 5, a semi infinite non conducting od (that is, infinite in one diection only), has unifom linea chage density. Show that the electic field Ep at point P makes an angle of 45 degees with the od and this esult is independent of the the distance. x d L d E (, )
11 ( x) + ( ) ( x) i ˆ + ( ) ˆ j ˆ x i ˆ ˆ j x + We can then compute the x and y components of the Electic Field. You may need dx (a + x ) 3/ x a a + x We can compute each integal and then take the limit as L goes to infinity. We find that in this limit, the components ae identical fo all. This means that the atio of these components is 1 and the angle is 45 degees fo all. E E x d ˆ dx (x + ) lim :L E x 1 dx (x + ) 1 + L 1 dx (x + ) 3/ L + L L + L lim L x i ˆ ˆ j x + x x + x dx (x + ) 3/ dx (x + ) 3/ 1 + x x + x L L.34 This poblem is woked out in detail in section 37 of the book. We also woked this poblem in detail in class. Please eview the deivation thee.
12 σ C / m.5 1 m z 1 1 m E z σ ε (1 z z + ) N / C.39 An electon is eleased fom est in a unifom electic field of magnitude. # 1 4 N/C. Calculate the acceleation of the electon (ignoe gavitation). F ma E 1.6 # 1 a m E 19 C 9.1 # 131 $. # 14 N/C 3.5 # 1 kg 15 m/s.47 In Millikan s expeiment, an oil dop of adius 1.64 µm and density ρ.851g / cm 3 is suspended in chambe C (Fig. 14) when a downwad electic field E N / C is applied. Find the chage on the dop in tems of e F E If the doplet is suspended, we know that the net foce is zeo. This means that the weight is balanced by an upwad electic foce. We wite this balance mg F E mg E mg mg E We can wite the mass in tems of the volume of the dop.
13 m ρ 4 3 π g cm π ( cm) g kg mg E kg 9.8m / s C N / C 5e
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 informationGauss Law. Physics 231 Lecture 21
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 informationF = 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 informationChapter 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 information2008 QuarterFinal Exam Solutions
2008 Quatefinal Exam  Solutions 1 2008 QuateFinal 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 informationSolutions to Homework Set #5 Phys2414 Fall 2005
Solution Set #5 1 Solutions to Homewok Set #5 Phys414 Fall 005 Note: The numbes in the boxes coespond to those that ae geneated by WebAssign. The numbes on you individual assignment will vay. Any calculated
More informationChapter 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 informationSamples 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 informationProblems 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 cuentcaying 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 information14. Gravitation Universal Law of Gravitation (Newton):
14. Gavitation 1 Univesal Law of Gavitation (ewton): The attactive foce between two paticles: F = G m 1m 2 2 whee G = 6.67 10 11 m 2 / kg 2 is the univesal gavitational constant. F m 2 m 1 F Paticle #1
More informationRevision 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 informationGauss 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 informationVoltage ( = Electric Potential )
V1 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 informationSo 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 informationThe 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 information2  ELECTROSTATIC POTENTIAL AND CAPACITANCE Page 1
 ELECTROSTATIC POTENTIAL AND CAPACITANCE Page. Line Integal of Electic Field If a unit positive chage is displaced by `given by dw E. dl dl in an electic field of intensity E, wok done is Line integation
More informationDeflection 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 informationMagnetic 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 informationChapter 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 informationChapter 4. Electric Potential
Chapte 4 Electic Potential 4.1 Potential and Potential Enegy... 43 4.2 Electic Potential in a Unifom Field... 47 4.3 Electic Potential due to Point Chages... 48 4.3.1 Potential Enegy in a System of
More informationXIIth 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 informationPhysics 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 informationForces & 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 informationNotes on Electric Fields of Continuous Charge Distributions
Notes on Electic Fields of Continuous Chage Distibutions Fo discete pointlike electic chages, the net electic field is a vecto sum of the fields due to individual chages. Fo a continuous chage distibution
More informationrotation  Conservation of mechanical energy for rotation  Angular momentum  Conservation of angular momentum
Final Exam Duing class (13:55 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 informationSolution 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 informationPhysics 202, Lecture 4. Gauss s Law: Review
Physics 202, Lectue 4 Today s Topics Review: Gauss s Law Electic Potential (Ch. 25Pat I) Electic Potential Enegy and Electic Potential Electic Potential and Electic Field Next Tuesday: Electic Potential
More informationCopyright 2008 Pearson Education, Inc., publishing as Pearson AddisonWesley.
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 informationChapter 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 (.11 T) i to ue a lage cuent flowing though a wie.
More informationPY1052 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 ighthand end. If H 6.0 m and h 2.0 m, what
More information2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses,
3.4. KEPLER S LAWS 145 3.4 Keple s laws You ae familia with the idea that one can solve some mechanics poblems using only consevation of enegy and (linea) momentum. Thus, some of what we see as objects
More informationGauss s law relates to total electric flux through a closed surface to the total enclosed charge.
Chapte : Gauss s Law Gauss s Law is an altenative fomulation of the elation between an electic field and the souces of that field in tems of electic flu. lectic Flu Φ though an aea ~ Numbe of Field Lines
More informationThe 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 informationmv2. Equating the two gives 4! 2. The angular velocity is the angle swept per GM (2! )2 4! 2 " 2 = GM . Combining the results we get !
Chapte. he net foce on the satellite is F = G Mm and this plays the ole of the centipetal foce on the satellite i.e. mv mv. Equating the two gives = G Mm i.e. v = G M. Fo cicula motion we have that v =!
More informationGeneral 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 informationIntroduction 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 informationPhysics 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 informationExam I. Spring 2004 Serway & Jewett, Chapters 15. Fill in the bubble for the correct answer on the answer sheet. next to the number.
Agin/Meye PART I: QUALITATIVE Exam I Sping 2004 Seway & Jewett, Chaptes 15 Assigned Seat Numbe Fill in the bubble fo the coect answe on the answe sheet. next to the numbe. NO PARTIAL CREDIT: SUBMIT ONE
More informationPY1052 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 informationVoltage ( = Electric Potential )
V1 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 informationPHYSICS 111 HOMEWORK SOLUTION #5. March 3, 2013
PHYSICS 111 HOMEWORK SOLUTION #5 Mach 3, 2013 0.1 You 3.80kg 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 informationLesson 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 informationGravitation. 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 informationExam 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 informationIntroduction 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 informationHour 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 information4.1 Cylindrical and Polar Coordinates
4.1 Cylindical and Pola Coodinates 4.1.1 Geometical Axisymmety A lage numbe of pactical engineeing poblems involve geometical featues which have a natual axis of symmety, such as the solid cylinde, shown
More informationPHYSICS 111 HOMEWORK SOLUTION #13. May 1, 2013
PHYSICS 111 HOMEWORK SOLUTION #13 May 1, 2013 0.1 In intoductoy physics laboatoies, a typical Cavendish balance fo measuing the gavitational constant G uses lead sphees with masses of 2.10 kg and 21.0
More informationMechanics 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 informationChapter 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 informationTheory and measurement
Gavity: Theoy and measuement Reading: Today: p11  Theoy of gavity Use two of Newton s laws: 1) Univesal law of gavitation: ) Second law of motion: Gm1m F = F = mg We can combine them to obtain the gavitational
More informationGravitation and Kepler s Laws Newton s Law of Universal Gravitation in vectorial. Gm 1 m 2. r 2
F Gm Gavitation and Keple s Laws Newton s Law of Univesal Gavitation in vectoial fom: F 12 21 Gm 1 m 2 12 2 ˆ 12 whee the hat (ˆ) denotes a unit vecto as usual. Gavity obeys the supeposition pinciple,
More information(References to) "Introduction to Electrodynamics" by David J. Griffiths 3rd ed., PrenticeHall, 1999. ISBN 013805326X
lectic Fields in Matte page. Capstones in Physics: lectomagnetism. LCTRIC FILDS IN MATTR.. Multipole xpansion A. Multipole expansion of potential B. Dipole moment C. lectic field of dipole D. Dipole in
More informationChapter 2 Coulomb s Law
Chapte Coulomb s Law.1 lectic Chage...3. Coulomb's Law...3 Animation.1: Van de Gaaff Geneato...4.3 Pinciple of Supeposition...5 xample.1: Thee Chages...5.4 lectic Field...7 Animation.: lectic Field
More informationMechanics 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 informationLesson 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 informationVector 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 informationPoynting Vector and Energy Flow in a Capacitor Challenge Problem Solutions
Poynting Vecto an Enegy Flow in a Capacito Challenge Poblem Solutions Poblem 1: A paallelplate capacito consists of two cicula plates, each with aius R, sepaate by a istance. A steay cuent I is flowing
More informationFluids Lecture 15 Notes
Fluids Lectue 15 Notes 1. Unifom flow, Souces, Sinks, Doublets Reading: Andeson 3.9 3.12 Unifom Flow Definition A unifom flow consists of a velocit field whee V = uî + vĵ is a constant. In 2D, this velocit
More informationIn the lecture on double integrals over nonrectangular domains we used to demonstrate the basic idea
Double Integals in Pola Coodinates In the lectue on double integals ove nonectangula domains we used to demonstate the basic idea with gaphics and animations the following: Howeve this paticula example
More informationReview 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 informationChapter 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 informationA r. (Can you see that this just gives the formula we had above?)
241 (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 informationNewton s Shell Theorem
Newton Shell Theoem Abtact One of the pincipal eaon Iaac Newton wa motivated to invent the Calculu wa to how that in applying hi Law of Univeal Gavitation to pheicallyymmetic maive bodie (like planet,
More information(Ch. 22.5) 2. What is the magnitude (in pc) of a point charge whose electric field 50 cm away has a magnitude of 2V/m?
Em I Solutions PHY049 Summe 0 (Ch..5). Two smll, positively chged sphees hve combined chge of 50 μc. If ech sphee is epelled fom the othe by n electosttic foce of N when the sphees e.0 m pt, wht is the
More informationv o a y = = * Since H < 1m, the electron does not reach to the top plate.
. The uniom electic ield between two conducting chged pltes shown in the igue hs mgnitude o.40 N/C. The plte seption is m, nd we lunch n electon om the bottom plte diectl upwd with v o 6 m/s. Will the
More informationCh. 8 Universal Gravitation. Part 1: Kepler s Laws. Johannes Kepler. Tycho Brahe. Brahe. Objectives: Section 8.1 Motion in the Heavens and on Earth
Ch. 8 Univesal Gavitation Pat 1: Keple s Laws Objectives: Section 8.1 Motion in the Heavens and on Eath Objectives Relate Keple s laws of planetay motion to Newton s law of univesal gavitation. Calculate
More informationCharges, 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 informationMagnetism: 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 Efield kq Efields ae ceated by chages: E = 2 Efield exets a foce on othe
More informationChapter 17 The Kepler Problem: Planetary Mechanics and the Bohr Atom
Chapte 7 The Keple Poblem: Planetay Mechanics and the Boh Atom Keple s Laws: Each planet moves in an ellipse with the sun at one focus. The adius vecto fom the sun to a planet sweeps out equal aeas in
More informationA) 2 B) 2 C) 2 2 D) 4 E) 8
Page 1 of 8 CTGavity1. m M Two spheical masses m and M ae a distance apat. The distance between thei centes is halved (deceased by a facto of 2). What happens to the magnitude of the foce of gavity between
More informationToday in Physics 217: multipole expansion
Today in Physics 17: multipole expansion Multipole expansions Electic multipoles and thei moments Monopole and dipole, in detail Quadupole, octupole, Example use of multipole expansion as appoximate solution
More informationFXA 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 informationUNIT 21: ELECTRICAL AND GRAVITATIONAL POTENTIAL Approximate time two 100minute sessions
Name St.No.  Date(YY/MM/DD) / / Section Goup# UNIT 21: ELECTRICAL AND GRAVITATIONAL POTENTIAL Appoximate time two 100minute sessions OBJECTIVES I began to think of gavity extending to the ob of the moon,
More informationMoment and couple. In 3D, because the determination of the distance can be tedious, a vector approach becomes advantageous. r r
Moment and couple In 3D, 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 informationPhysics 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 informationProblem Set 6: Solutions
UNIVESITY OF ALABAMA Depatment of Physics and Astonomy PH 164 / 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 information9. 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 informationEpisode 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(a) The centripetal acceleration of a point on the equator of the Earth is given by v2. The velocity of the earth can be found by taking the ratio of
Homewok VI Ch. 7  Poblems 15, 19, 22, 25, 35, 43, 51. Poblem 15 (a) The centipetal acceleation of a point on the equato of the Eath is given by v2. The velocity of the eath can be found by taking the
More informationCHAPTER 5 GRAVITATIONAL FIELD AND POTENTIAL
CHATER 5 GRAVITATIONAL FIELD AND OTENTIAL 5. Intoduction. This chapte deals with the calculation of gavitational fields and potentials in the vicinity of vaious shapes and sizes of massive bodies. The
More information1240 ev nm 2.5 ev. (4) r 2 or mv 2 = ke2
Chapte 5 Example The helium atom has 2 electonic enegy levels: E 3p = 23.1 ev and E 2s = 20.6 ev whee the gound state is E = 0. If an electon makes a tansition fom 3p to 2s, what is the wavelength of the
More informationChapter 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 informationExperiment 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 informationPhys 2101 Gabriela González. cos. sin. sin
1 Phys 101 Gabiela González a m t t ma ma m m T α φ ω φ sin cos α τ α φ τ sin m m α τ I We know all of that aleady!! 3 The figue shows the massive shield doo at a neuton test facility at Lawence Livemoe
More informationGravity and the figure of the Earth
Gavity and the figue of the Eath Eic Calais Pudue Univesity Depatment of Eath and Atmospheic Sciences West Lafayette, IN 479071397 ecalais@pudue.edu http://www.eas.pudue.edu/~calais/ Objectives What is
More informationMultiple 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 informationMultiple 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 informationUniform 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 111 Engineeing Mechanics : Dynamics
More informationPhysics 505 Homework No. 5 Solutions S51. 1. Angular momentum uncertainty relations. A system is in the lm eigenstate of L 2, L z.
Physics 55 Homewok No. 5 s S5. Angula momentum uncetainty elations. A system is in the lm eigenstate of L 2, L z. a Show that the expectation values of L ± = L x ± il y, L x, and L y all vanish. ψ lm
More informationCoordinate 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 informationAlgebra and Trig. I. A point is a location or position that has no size or dimension.
Algeba and Tig. I 4.1 Angles and Radian Measues A Point A A B Line AB AB A point is a location o position that has no size o dimension. A line extends indefinitely in both diections and contains an infinite
More information1. CIRCULAR MOTION. ω =
1. CIRCULAR MOION 1. Calculate the angula elocity and linea elocity of a tip of minute hand of length 1 cm. 6 min. 6 6 s 36 s l 1 cm.1 m ω?? Fomula : ω π ω ω π 3.14 36 ω 1.744 1 3 ad/s ω.1 1.74 1 3 1.74
More informationLab M4: The Torsional Pendulum and Moment of Inertia
M4.1 Lab M4: The Tosional Pendulum and Moment of netia ntoduction A tosional pendulum, o tosional oscillato, consists of a disklike mass suspended fom a thin od o wie. When the mass is twisted about the
More informationLearning 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 informationChapter 22 Solutions
PHY49 Chapte Solutions Poblem : A +5 micoc chage is located 4 cm fom a +3 micoc chage The magnitude of the electostatic foce on the lage chage and on the smalle chage (in N) is espectively Answe: 5 5 Solution:
More informationAP 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 informationCarterPenrose diagrams and black holes
CatePenose diagams and black holes Ewa Felinska The basic intoduction to the method of building Penose diagams has been pesented, stating with obtaining a Penose diagam fom Minkowski space. An example
More informationChapter 4. Gauss s Law
Chapte 4 Gauss s Law 4.1 lectic Flux...44. Gauss s Law...43 xample 4.1: Infinitely Long Rod of Unifom Chage Density...48 xample 4.: Infinite Plane of Chage...49 xample 4.3: Spheical Shell...41 xample
More informationFunctions of a Random Variable: Density. Math 425 Intro to Probability Lecture 30. Definition Nice Transformations. Problem
Intoduction One Function of Random Vaiables Functions of a Random Vaiable: Density Math 45 Into to Pobability Lectue 30 Let gx) = y be a onetoone function whose deiatie is nonzeo on some egion A of the
More information