Problem Set 6: Solutions

Size: px
Start display at page:

Download "Problem Set 6: Solutions"

Transcription

1 UNIVESITY OF ALABAMA Depatment of Physics and Astonomy PH 16-4 / LeClai Fall 28 Poblem Set 6: Solutions 1. Seway Potons having a kinetic enegy of 5. MeV ae moving in the positive x diection and ente a magnetic field B =.5 ˆk T diected out of the plane of the page and extending fom x = to x=1. m, as shown below. (a) Calculate the y component of the potons momentum as they leave the magnetic field. (b) Find the angle α between the initial velocity vecto afte the beam emeges fom the field. Note that 1 ev= J. Bout Figue 1: Poblem 1 Fist of all, we know that once the poton entes the egion of magnetic field it will follow a cicula path of adius, and once it leaves the egion it will once again move in a staight line path, tangential to the cicula path in the field egion. We will need to use some geomety to elate α to the given distance x and the adius of the cicula path. Then we will detemine the adius of the cicula path in tems of the known kinetic enegy, and we will be good to go... efe to the figue below: d 9-α β α Figue 2: Poblem 1 Solution The path of the potons in the egion of magnetic field is cicula, and descibed by a adius. The potons will move though the egion of magnetic field acoss its lateal distance d, and this will define an angle α, caving out an ac of a cicle of adius. We can define a ight tiangle by the cente of

2 the cicle defining the path in the magnetic field egion, the point at which the potons ente the field, and the point at which they leave. The angle at which the potons leave the field with espect to the hoizontal is then β =α based on the geomety of the figue above. Once we know, given d, we can find α by noting sin α=d/. The adius of the cicula path of the potons can be found by noting that the centipetal foce (keeping them in a cicula path) must be povided by the magnetic foce. Note that a poton has chage e and mass m p, and let the poton s velocity be v. Also ecall that magnetic foces do no wok, so the potons velocity will not change in magnitude afte passing though the egion of magnetic field. Since the motion of the paticle is always at a ight angle with espect to the field, we can just deal in magnitudes. F cent = m pv 2 = F B = evb sin θ Bv = evb = = m pv eb = p eb Hee p is the magnitude of the potons momentum. Now we have the adius of the path in tems of the field, the chage on a poton, and the potons momentum. We ae given the potons kinetic enegy K, which is elated to its momentum by K =p 2 /2m p. Thus, = p eb = 2mp K eb 6.46 m emembe that 1 ev= J to make the units come out popely. Given the adius, we can now find the angle α: sin α = d = α = sin 1 d 8.9 Now, since the magnetic foce does no wok, the potons momentum does not change in magnitude, so the initial and final momentum ae the same. The vetical (y) component of the potons momentum can thus be easily found: p y =p sin α p y = p sin α = 2m p K sin α kg m/s 2. Seway Conside an electon obiting a poton and maintained in a fixed cicula path of adius = m by the Coulomb foce. Teating the obiting chage as a cuent loop, calculate the esulting toque when the system is in a magnetic field of.4 T diected pependicula to the magnetic moment of the electon. Fist, need to know the cuent that coesponds to one obiting electon. Fom the cuent I, magnetic field B, and the obital adius we can find the toque. An electon in a cicula obit of adius has a peiod of T = 2π/v, whee v it he electon s velocity. If a single electon chage e obits once evey T seconds, then the cuent is by definition I = q t = e T = ev 2π

3 We can find the velocity fom the condition fo cicula motion. The only foce pesent (that we know of) is the electic foce, which must then povide the centipetal foce on the electon. The electic foce is just that of two point chages e and e sepaated by a distance. F cent F E = m ev 2 k ee 2 k e e 2 = = v = 2 m e We can now substitute this in ou expession fo cuent above: I = ev 2π = e k e e 2 2π m e = e2 ke 2π m e 3 Finally, since the magnetic field is pependicula to the electon s magnetic moment, the magnitude of the toque is given by τ = IAB whee A is the aea of the cuent loop" fomed by the obiting electon, A=π 2. Thus, τ = IAB = e2 ke 2π m e 3 π2 B = 1 ke 2 e2 B m e N m The negative sign eminds us that cuent is the diection that positive chage flows, and thus the diection of the toque is given by the ight hand ule consistent with the cuent, which is opposite the diection that the electon obits. 3. Ohanian 29.5 A wie lying along the x axis caies a cuent of 3 A in the +x diection. A poton at = 2.5 ŷ has instantaneous velocity v = 2. ˆx 3. ŷ + 4. ẑ, whee is in metes and v in metes pe second. What is the instantaneous magnetic foce on this poton? If the cuent flows along the ˆx diection, and the poton is diectly above the wie in the ŷ diection, then the magnetic field must be pointing along the ẑ diection at the poton s position. Thus, the magnetic field at the poton s position is given by B = µ oi 2π ẑ B z ẑ Finding the magnetic foce is now just a matte of calculating the coss poduct v B and multiplying by the poton s chage e. Fist, the coss poduct: ˆx ŷ ẑ v B = det v x v y v z B x B y B z = det ˆx ŷ ẑ 2 m/s 3 m/s 4 m/s B z = 3B z ˆx 2B z ŷ m/s Thus, the magnetic foce is F B = q v B = 3eB z ˆx 2eB z ŷ m/s ( ) (3 ˆx + 2 ŷ) N If you note that 1 T = 1 kg/s 2 A, you should be able to make the units come out popely. Fo

4 completion, the magnitude of the foce is then F B = ( ) N 4. Ohanian The electic field of a long, staight line of chage with λ coulombs pe mete is E = 2k eλ whee is the distance fom the wie. Suppose we move this line of chage paallel to itself at speed v. (a) The moving line of chage constitutes an electic cuent. What is the magnitude of this cuent? (b) What is the magnitude of the magnetic field poduced by this cuent? (c) Show that the magnitude of the magnetic field is popotional to the magnitude of the electic field, and find the constant of popotionality. The cuent can be found by thinking about how much chage passes though a given egion of space pe unit time. If we wee standing next to the wie, in a time t, the length of wie that passes by us would be v t. The coesponding chage is then q =λv t, and thus the cuent is I = q t = λv t = λv t Fom the cuent, we can easily find the magnetic field a distance fom the wie. B = µ oi 2π = µ oλv 2π If the wie wee sitting still (o we wee taveling paallel to it at the same velocity v), it would poduce the electic field given above. eaanging the given expession, we can elate λ and E, λ = E/2k e. Substituting this in ou expession fo the magnetic field, B = µ oλv 2π = µ oev 4πk e = µ oɛ o ve Fo the last step, we noted that ɛ o =1/4πk e. 5. Pucell 7.14 A metal cossba of mass m slides without fiction on two long paallel ails a distance b apat. A esisto is connected acoss the ails at one end; compaed with, the esistance of the ba and ails is negligible. Thee is a unifom field B pependicula to the plane of the figue. At time t=, the cossba is given a velocity v o towad the ight. What happens then? (a) Does the od eve stop moving? If so, when? (b) How fa does it go? (c) How about consevation of enegy? Hint: fist find the acceleation, and make use of an instantaneous balance of powe.

5 B in v o b Figue 3: Poblem 5 The moving od foms a closed loop with the ails, and once the od stats moving, the aea of this loop inceases with time. With a constant magnetic field, this means that the magnetic flux is inceasing with time, and theefoe thee must be an induced voltage. Let the position of the od be x, with the ˆx diection being to the ight, and the ŷ diection upwad. This means the magnetic field points in the ẑ diection, giving in a magnitude B. At time t=, we will say the od has velocity v o and position x o. Fo any time t, we will just call the velocity v and position x, since we don t know what they ae yet. The induced voltage can be found fom the magnetic flux though the loop, which is itself is easily found, since the magnetic field is constant and eveywhee pependicula to the plane of the loop. We only need the aea of the loop. If the width of the loop is b, and the position of the od is x, the aea is just bx, and that is enough to find the flux: Φ B = B d A = B d A = BA = Bxb loop loop The induced voltage is found fom the time vaiation of the flux via Faaday s law. The induced voltage - which is now applied to the esisto - will lead to a counteclockwise cuent in the loop, since it wants to stop the incease in flux by ceating a magnetic field opposing the extenal magnetic field. V = dφ B dt = Bb dx dt = Bbv = I The pesence of a cuent in the conducting od will lead to a magnetic foce. Since the field is into the page ( ẑ diection), and the cuent is flowing up though though the od (ŷ diection), the foce must be in the ŷ diection. F B = I L B = IbB ŷ ( ẑ) = IbB ˆx = B2 b 2 v = ma ecall that the diection of L is the same as the diection of the cuent. Since the magnetic foce is the only foce acting on the od (in the absence of fiction), it must also give the acceleation of the od, as indicted in the last step. Incidentally, we could have gotten hee much moe quickly with a little intuition. If we ecognize that thee must be a cuent flowing in the esisto due to the induced voltage caused by the motion of the od, then we know thee is powe dissipated in the esisto. This powe must be the same as that supplied to the od. The mechanical powe is F v, and the electical powe is I 2. Consevation of enegy equies that these two powes be equal, which along with the motional voltage leads diectly to the equation above.

6 Anyway: now we have a small equation elating v and its ate of change, dv/dt=a. We can solve it by sepaation of vaiables, which is totally cool since none of ou quantities ae zeo. Dividing by zeo is not cool. B2 b 2 v = mdv dt m dv B 2 b 2 v = dt Now we ve got something we can integate. Ou stating condition is velocity v o at time t ==, going until some late time t whee the velocity is v. v v o m dv t B 2 b 2 v = m B 2 b 2 ln v v v o = t m B 2 b 2 ln v v o = t dt t = v = v o e t/τ with τ = m B 2 b 2 The velocity is an exponentially deceasing function of time, which means it neve stops moving - the velocity appoaches, but does not each, zeo. The od will also appoach a final taget displacement in spite of this fact, which we can find eadily by integating the velocity. x = o v dt = o ( ) v o e t/τ = v o τe t/τ = v o τ = mv o B 2 b 2 Once again, if you note that 1 T = 1 kg/s 2 A and 1 V 1 A = 1 W, you should be able to make the units come out coectly. Finally, we can calculate the total electical enegy expended. The electical powe dissipated in the esisto is P = du/dt = I 2, so the tiny bit of potential enegy du expended in a time dt is du = I 2 dt. We can integate ove all times to find the total potential enegy. o U = I 2 dt = = B2 b 2 v 2 o = 1 2 mv2 ( Bbv ) 2 dt = B2 b 2 e 2t/τ dt = B2 b 2 v 2 o v 2 dt ( τ 2 e 2t/τ ) = B2 b 2 v 2 o ( ) m 2B 2 b 2 As we would expect fom consevation of enegy, all of the initial kinetic enegy of the conducting ba ends up dissipated in the esisto.

7 6. Seway A unifom magnetic field of magnitude.15 T is diected along the positive x axis. A positon (a positively-chaged electon) moving at m/s entes the field along a diection that makes an angle of 85 with the x axis. The motion of the paticle is expected to be a helix in this case. Calculate the pitch p and adius of the tajectoy. y v z 85 p B x Figue 4: Poblem 6 The fist thing to ealize is that a helix is basically a cuve descibed by cicula motion in one plane, in this case the y z plane, and linea motion along the pependicula diection, in this case the x axis. A helix of cicula adius a and pitch p can be descibed paametically by x(t) = pt 2π y(t) = a cos t z(t) = a sin t As we can see, the motion in the y z plane obeys y 2 + z 2 = a 2, descibing a cicle of adius a, and along the x axis we just have constant velocity motion. Since the x, y, and z motions ae uncoupled (e.g., the equation fo x(t) has no y s o z s in it), things ae in fact petty simple. The cicula motion comes fom the component of the velocity pependicula to the magnetic field, the component of velocity lying in the y z plane, which we will call v. The pitch is just how fa fowad along the x axis the paticle moves in one peiod of cicula motion T. Thus, if the velocity along the x axis is v x, p = v x T = (v cos 85 ) T We have aleady discoveed that the peiod and adius of cicula motion fo a paticle in a magnetic field does not depend on the paticle s velocity, it only mattes that thee is always a velocity component pependicula to the magnetic field T = 2πm qb and = mv qb Putting eveything togethe,

8 p = 2πmv cos m Bq = mv qb sin m By the way, hee is an inteesting tidbit fom MathWold: i A helix, sometimes also called a coil, is a cuve fo which the tangent makes a constant angle with a fixed line. The shotest path between two points on a cylinde (one not diectly above the othe) is a factional tun of a helix, as can be seen by cutting the cylinde along one of its sides, flattening it out, and noting that a staight line connecting the points becomes helical upon e-wapping. It is fo this eason that squiels chasing one anothe up and aound tee tunks follow helical paths. i

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

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

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

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

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

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

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

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

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

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

2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses,

2 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 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

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

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

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

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

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

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

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

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

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

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

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

Solutions to Homework Set #5 Phys2414 Fall 2005

Solutions 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 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

mv2. 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 !

mv2. 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 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Exam I. Spring 2004 Serway & Jewett, Chapters 1-5. Fill in the bubble for the correct answer on the answer sheet. next to the number.

Exam I. Spring 2004 Serway & Jewett, Chapters 1-5. 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 1-5 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 information

Set 3: 120 N/m units 0.25 Kg. 1A The unit of the damping constant is a) Kg/s b) N/m c) N d) Joule/s e) NA

Set 3: 120 N/m units 0.25 Kg. 1A The unit of the damping constant is a) Kg/s b) N/m c) N d) Joule/s e) NA 05/05/04 PHYSICS 3 Exa #1 NAME Please wite down you nae also on the back side of this exa 1. Hee ae thee sets of values fo the sping constant k, daping constant b, and ass fo thee daped oscillatos: Set

More information

1.1 KINEMATIC RELATIONSHIPS

1.1 KINEMATIC RELATIONSHIPS 1.1 KINEMATIC RELATIONSHIPS Thoughout the Advanced Highe Physics couse calculus techniques will be used. These techniques ae vey poweful and knowledge of integation and diffeentiation will allow a deepe

More information

Ch. 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 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 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

PHYSICS 111 HOMEWORK SOLUTION #13. May 1, 2013

PHYSICS 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 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

Seventh Edition DYNAMICS 15Ferdinand P. Beer E. Russell Johnston, Jr. Lecture Notes: J. Walt Oler Texas Tech University

Seventh Edition DYNAMICS 15Ferdinand P. Beer E. Russell Johnston, Jr. Lecture Notes: J. Walt Oler Texas Tech University Seenth 15Fedinand P. ee E. Russell Johnston, J. Kinematics of Lectue Notes: J. Walt Ole Texas Tech Uniesity Rigid odies CHPTER VECTOR MECHNICS FOR ENGINEERS: YNMICS 003 The McGaw-Hill Companies, Inc. ll

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

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

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

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

Gravitation and Kepler s Laws Newton s Law of Universal Gravitation in vectorial. Gm 1 m 2. r 2

Gravitation 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

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

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

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

Geostrophic balance. John Marshall, Alan Plumb and Lodovica Illari. March 4, 2003

Geostrophic balance. John Marshall, Alan Plumb and Lodovica Illari. March 4, 2003 Geostophic balance John Mashall, Alan Plumb and Lodovica Illai Mach 4, 2003 Abstact We descibe the theoy of Geostophic Balance, deive key equations and discuss associated physical balances. 1 1 Geostophic

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

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

Classical Lifetime of a Bohr Atom

Classical Lifetime of a Bohr Atom 1 Poblem Classical Lifetime of a Boh Atom James D. Olsen and Kik T. McDonald Joseph Heny Laboatoies, Pinceton Univesity, Pinceton, NJ 85 (Mach 7, 5) In the Boh model of the hydogen atom s gound state,

More information

1240 ev nm 2.5 ev. (4) r 2 or mv 2 = ke2

1240 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 information

Lesson 32: Measuring Circular Motion

Lesson 32: Measuring Circular Motion Lesson 32: Measuing Cicula Motion Velocity hee should be a way to come up with a basic fomula that elates velocity in icle to some of the basic popeties of icle. Let s ty stating off with a fomula that

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

7 Circular Motion. 7-1 Centripetal Acceleration and Force. Period, Frequency, and Speed. Vocabulary

7 Circular Motion. 7-1 Centripetal Acceleration and Force. Period, Frequency, and Speed. Vocabulary 7 Cicula Motion 7-1 Centipetal Acceleation and Foce Peiod, Fequency, and Speed Vocabulay Vocabulay Peiod: he time it takes fo one full otation o evolution of an object. Fequency: he numbe of otations o

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

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

LINES AND TANGENTS IN POLAR COORDINATES

LINES AND TANGENTS IN POLAR COORDINATES LINES AND TANGENTS IN POLAR COORDINATES ROGER ALEXANDER DEPARTMENT OF MATHEMATICS 1. Pola-coodinate equations fo lines A pola coodinate system in the plane is detemined by a point P, called the pole, and

More information

Algebra and Trig. I. A point is a location or position that has no size or dimension.

Algebra 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 information

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

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

More information

Determining solar characteristics using planetary data

Determining solar characteristics using planetary data Detemining sola chaacteistics using planetay data Intoduction The Sun is a G type main sequence sta at the cente of the Sola System aound which the planets, including ou Eath, obit. In this inestigation

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

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

Chapter 8, Rotational Kinematics. Angular Displacement

Chapter 8, Rotational Kinematics. Angular Displacement Chapte 8, Rotational Kinematics Sections 1 3 only Rotational motion and angula displacement Angula velocity and angula acceleation Equations of otational kinematics 1 Angula Displacement! B l A The length

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

(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 information

Resources. Circular Motion: From Motor Racing to Satellites. Uniform Circular Motion. Sir Isaac Newton 3/24/10. Dr Jeff McCallum School of Physics

Resources. Circular Motion: From Motor Racing to Satellites. Uniform Circular Motion. Sir Isaac Newton 3/24/10. Dr Jeff McCallum School of Physics 3/4/0 Resouces Cicula Motion: Fom Moto Racing to Satellites D Jeff McCallum School of Physics http://www.gap-system.og/~histoy/mathematicians/ Newton.html http://www.fg-a.com http://www.clke.com/clipat

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

SELF-INDUCTANCE AND INDUCTORS

SELF-INDUCTANCE AND INDUCTORS MISN-0-144 SELF-INDUCTANCE AND INDUCTORS SELF-INDUCTANCE AND INDUCTORS by Pete Signell Michigan State Univesity 1. Intoduction.............................................. 1 A 2. Self-Inductance L.........................................

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

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

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

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

A) 2 B) 2 C) 2 2 D) 4 E) 8

A) 2 B) 2 C) 2 2 D) 4 E) 8 Page 1 of 8 CTGavity-1. 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 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

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

2 - ELECTROSTATIC POTENTIAL AND CAPACITANCE Page 1

2 - 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 information

Rotation. Problem solving strategy is the same as for problems with linear motion... Rotation

Rotation. Problem solving strategy is the same as for problems with linear motion... Rotation Rotation The basic quantity in otation is the angula displacement simila ole to the linea displacement studied in chapte units: adians, eolutions, degees, θ Poblem soling stategy is the same as fo poblems

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

Section 5-3 Angles and Their Measure

Section 5-3 Angles and Their Measure 5 5 TRIGONOMETRIC FUNCTIONS Section 5- Angles and Thei Measue Angles Degees and Radian Measue Fom Degees to Radians and Vice Vesa In this section, we intoduce the idea of angle and two measues of angles,

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

In this section we shall look at the motion of a projectile MOTION IN FIELDS 9.1 PROJECTILE MOTION PROJECTILE MOTION

In this section we shall look at the motion of a projectile MOTION IN FIELDS 9.1 PROJECTILE MOTION PROJECTILE MOTION MOTION IN FIELDS MOTION IN FIELDS 9 9. Pojectile motion 9. Gavitational field, potential and enegy 9.3 Electic field, potential and enegy 9. PROJECTILE MOTION 9.. State the independence of the vetical

More information

TORQUE AND ANGULAR MOMENTUM IN CIRCULAR MOTION

TORQUE AND ANGULAR MOMENTUM IN CIRCULAR MOTION MISN-0-34 TORQUE AND ANGULAR MOMENTUM IN CIRCULAR MOTION shaft TORQUE AND ANGULAR MOMENTUM IN CIRCULAR MOTION by Kiby Mogan, Chalotte, Michigan 1. Intoduction..............................................

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

Today in Physics 217: multipole expansion

Today 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 information

Phys 2101 Gabriela González. cos. sin. sin

Phys 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 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

14. Gravitation Universal Law of Gravitation (Newton):

14. 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 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