Electricity and Magnetism Isolated Conductors and Potential Dipole in an Electric field Millikan s Experiment

Transcription

1 Electricity and Magnetism Isolated Conductors and Potential Dipole in an Electric field Millikan s Experiment Lana Sheridan De Anza College Jan 25, 2018

2 Last time relation between E-field and potential potential from many charges potential around continuous charge distributions

3 Warm Up Questions What is an alternative unit for the electric field? (A) Vm (B) V/m (C) V/m 2

4 Warm Up Questions What is an alternative unit for the electric field? (A) Vm (B) V/m (C) V/m 2

5 Overview Potential of charged conductor torque on a dipole in an E-field potential energy of a dipole in an E-field Millikan s experiment

6 Conductor in an Electric field The E-field inside an isolated conductor at equilibrium is zero. eg. an isolated conductor with excess charge: E = 0 1 Figure from Openstax College Physics.

7 Potential due 762 to an IsolatedChapter Charged 25 Electric Conductor Potential What is the potential at the point R? a R perpendicular to t Equation 25.3, we essarily zero: b k e Q R V k e Q r This result applies where on the surfa c E R k e Q r 2 r r the surface of a potential surfac librium is at th field is zero insi inside the cond

8 ming a small hole exists e Potential no net electric dueforce to an actsisolated Charged Conductor PART otential at all points inside r (m) SOLATED g a All excess shows. CONDUCTOR charge flows to the outside, 645 in the interior, the electric field is zero. (a) with radial distance for the l.the curves 12 of Fig b entiating with respect to r, 12 tant is zero). The curve of b by integrating with 8 V (kv) 4 E (kv/m) r (m) r (m) (a) (b) Since V = E ds the potential inside the conductor is Fig (a) A plot of V(r) both constant. 12 inside and outside a charged spherical shell of radius 1.0 m. (b) A plot of 1 Figure from Halliday, Resnick, Walker, 9th ed.

9 inside is zero. We now generate another property of a charged c The electric potential potential. is constant Consider everywhere two points on a conductor and on the surfa (including the surface!), shown but in Figure the charge distribution Along a surface may vary. path connect Charge distribution on a conductor Notice from the spacing of the positive signs that the surface charge density is nonuniform. S E Figure An arbitra positive charge. When the librium, all the charge res the conductor, and the dir the conductor is perpendi potential is constant inside potential at the surface.

10 Charge distribution on a conductor An illustrative example (25.8), electric field around conductor. r 1 At all points on the object V is constant. q 1 V 1 = V 2 k e q 1 = k eq 2 r 1 r 2 q 1 = r 1 q 2 r 2 q 2 r 2 Since r 1 > r 2, q 1 > q 2. sharper curvature of surface, higher charge density

11 Question: Charge Density q 1 r 1 V 1 = V 2 k e q 1 = k eq 2 r 1 r 2 q 1 = r 1 q 2 r 2 q 2 r 2 What is the ratio of the surface charge densities σ 1 /σ 2 on the spheres? (A) r 1 r2 (B) r 2 1 r 2 2 igure (Example 25.8) Two harged spherical conductors connected y a conducting wire. The spheres are at (C) r 2 r1 (D) r 3 2 r 3 1

12 Question: Charge Density q 1 r 1 V 1 = V 2 k e q 1 = k eq 2 r 1 r 2 q 1 = r 1 q 2 r 2 What is the ratio of the surface charge densities σ 1 /σ 2 on the spheres? (A) r 1 r2 q 2 igure (Example 25.8) Two harged spherical conductors connected y a conducting wire. The spheres are at r 2 (B) r 2 1 r 2 2 (C) r 2 r1 (D) r 3 2 r 3 1

13 Charge distribution on a conductor An illustrative example (25.8), electric field around conductor. r 1 At all points on the object V is constant. q 1 V 1 = V 2 E 1 r 1 = E 2 r 2 E 1 E 2 = r 2 r 1 Since r 2 < r 1, E 1 < E 2. q 2 r 2 sharper curvature of surface, stronger electric field

14 Corona Discharge A corona discharge occurs when a conductor at a very high potential ionizes a fluid (eg. air) that surrounds it. The fields that form around sharp edges of the conductor are high enough to form small plasma regions, but not full electric breakdown.

15 Corona Discharge A corona discharge occurs when a conductor at a very high potential ionizes a fluid (eg. air) that surrounds it. The fields that form around sharp edges of the conductor are high enough to form small plasma regions, but not full electric breakdown. responsible for significant power losses in high voltage lines useful for pool sanitation ozone manufacture ionizers air purifiers nitrogen lasers (TEA lasers)

16 Coronal Discharge 1 Photo Wartenburg Pinwheel by Giles Read kV

17 Corona Discharge Fork in a microwave. (Microwave ovens generate electric fields.)

18 Potential Energy: Electric Dipole in an E-Field Remember: electric dipole A pair of charges of equal magnitude q but opposite sign, separated by a distance, d. 594 CHAPTER 22 ELECTRIC FIELDS A water molecule is an example Hydrogen Positive side p 105 Oxygen Negative side Hydrogen Fig A molecule of H 2 O, showing the three nuclei (represented by dots) and 22-9 A Dipole We have defined the points from the nega of a dipole in a unifo of the two vectors E : A molecule of the black dots repr hydrogen nuclei (h the regions in which In a water mo lie on a straight lin

19 electric field is uniform, those forces act in op Fig a) and with the same magnitude F uniform, the net force on the dipole from the fiel of the dipole does not move. However, the forces anet torque : t on the dipole about its center of m the line connecting the charged ends, at some di adistance d x from the other end. From Eq. 10 the magnitude of the net torque : t as Electric Dipole in an Electric Field (26.6) Because the net charge of a dipole is zero, the net force is zero also. But there is a torque! is the angle between the p and E F q d p com E +q F t Fx sin u F(d x) sin u We can also write the magnitude of t : in term tric field E and the dipole moment p qd.to do p/q for d in Eq , finding that the magnitude o t pe sin u. We can generalize this equation to vector form as (a) : p : E : (torque on a τ p Fig The dipole is being torqued into alignment. (b) E (a) An electric dipole in a E : Vectors p : and are shown in Fig b.The to rotate p : (hence the dipole) into the direction of Fig , such rotation is clockwise. As we discu resent a torque that gives rise to a clockwise rot with the magnitude of the torque. With that notati t pe sin u.

20 electric field is uniform, those forces act in op Fig a) and with the same magnitude F uniform, the net force on the dipole from the fiel of the dipole does not move. However, the forces anet torque : t on the dipole about its center of m the line connecting the charged ends, at some di adistance d x from the other end. From Eq. 10 the magnitude of the net torque : t as Electric Dipole in an Electric Field (26.6) Because the net charge of a dipole is zero, the net force is zero also. But there is a torque! is the angle between the p and E d E q F +q F p com τ = r F t Fx sin u F(d x) sin u = 2(d/2)(qE) sin [clockwise] We can also write the magnitude of : t in term tric field E and the dipole moment p qd.to do p/q for d in Eq , finding that the magnitude o and p = qd τ = pe sin [clockwise] t pe sin u. We can generalize this equation to vector form as τ p Fig (a) The dipole is being torqued into alignment. (b) E (a) An electric dipole in a In general, E : : p : E : (torque on a Vectors p : and are shown in Fig b.The to rotate p : (hence the dipole) into the direction of Fig , such rotation is clockwise. As we discu resent a torque τ = that p gives E rise to a clockwise rot with the magnitude of the torque. With that notati t pe sin u.

21 Electric Dipole in an Electric Field (26.6) We can also find an expression for the potential energy of a dipole in an E-field. Define U = 0 when = π 2 (the dipole is to the field lines). For a conservative force: U = W int U() 0 U(π/2) = τ d U() = π/2 π/2 τd where the minus sign inside the integral is due to τ being clockwise, while increases counter clockwise. can be positive or negative. U = pe[ cos ] π/2 = pe cos U = p E

22 ins water n, the mi- le is least electric dipole in an external electric energy Question: is Electric Dipole in an Electric Field field. Rank the orientations according The figure shows to (a) four the orientations magnitude of of an electric the torque dipoleonin an external electric the field. dipole Rank and the (b) orientations the potential according energy to the magnitude of the dipole, torque on greatest the dipole, first. greatest first. tation u f, (22-39) tation is nt), then the work (22-40) (A) 1, 2, 3, 4 (1) (3) (B) (1 and 3), (2 and 4) (C) (2 and 4), (1 and 3) (D) all the same Page 595, Halliday, Resnick, Walker. (2) E (4)

23 ins water n, the mi- le is least electric dipole in an external electric energy Question: is Electric Dipole in an Electric Field field. Rank the orientations according The figure shows to (a) four the orientations magnitude of of an electric the torque dipoleonin an external electric the field. dipole Rank and the (b) orientations the potential according energy to the magnitude of the dipole, torque on greatest the dipole, first. greatest first. tation u f, (22-39) tation is nt), then the work (22-40) (A) 1, 2, 3, 4 (1) (3) (B) (1 and 3), (2 and 4) (C) (2 and 4), (1 and 3) (D) all the same Page 595, Halliday, Resnick, Walker. (2) E (4)

24 ins water n, the mi- le is least electric dipole in an external electric energy Question: is Electric Dipole in an Electric Field field. Rank the orientations according The figure shows to (a) four the orientations magnitude of of an electric the torque dipoleonin an external electric the field. dipole Rank and the (b) orientations the potential according energy to the potential energy of the of dipole, the dipole, greatest greatest first. first. tation u f, (22-39) tation is nt), then the work (22-40) (A) 1, 2, 3, 4 (1) (3) (B) (1 and 3), (2 and 4) (C) (2 and 4), (1 and 3) (D) all the same Page 595, Halliday, Resnick, Walker. (2) E (4)

25 ins water n, the mi- le is least electric dipole in an external electric energy Question: is Electric Dipole in an Electric Field field. Rank the orientations according The figure shows to (a) four the orientations magnitude of of an electric the torque dipoleonin an external electric the field. dipole Rank and the (b) orientations the potential according energy to the potential energy of the of dipole, the dipole, greatest greatest first. first. tation u f, (22-39) tation is nt), then the work (22-40) (A) 1, 2, 3, 4 (1) (3) (B) (1 and 3), (2 and 4) (C) (2 and 4), (1 and 3) (D) all the same Page 595, Halliday, Resnick, Walker. (2) E (4)

26 Microwave Ovens An application of the fact that a dipole experiences a torque in an electric field is microwave cooking. Microwave ovens produce electric fields that change direction rapidly. Since water molecules are dipoles, they begin to rotate to align with the field, back and forth. This motion becomes thermal energy in the food.

27 sign and given in r physics Van de Graaf generator y means w metal eans of rid. The positive eedles at e charge In pracrical disis about ential of s radius s 20 milreceive us target ms. If a generaon s hair as in the Metal dome P Ground Belt Insulator Can (in principle) build up to 3 million Volts when used in air.

28 Milikan s Oil Drop Experiment The value of e, the basic unit of charge was found in this experiment. From Robert Millikan worked with Harvey Fletcher on the experiment. At the time the idea of both atoms and subatomic particles was only just gaining acceptance.

29 Milikan s Oil Drop Experiment Some history: early 1800s John Dalton realized chemical reactions could be explained if there were element-particles 1827 Robert Brown noticed that pollen particles vibrated randomly when viewed with a microscope early 1870s Ludwig Boltzmann explained thermodynamic behavior in terms of statistics of particles 1897 JJ Thompson discovered the electron in cathode rays ; noticed it had a charge and very small mass 1905 Albert Einstein explained Brown s Brownian motion in terms of atoms 1909 Ernest Rutherford s experiment done by Hans Geiger and Ernest Marsden discovered the nucleus

30 is overwhelmed by ultraviolet radiation from the Sun. Newly devel Milikan s Oil Drop Experiment l Oil droplets Pinhole d q S v Telescope with scale in eyepiece

31 Question In an experiment, a potential difference (voltage) of V = 10V is x supplied to a pair of conducting e plates separated by a distance d = 20 cm. What is the electric field strength between the plates? E field that other charges h not the field set up by t acting on the particle in particle or object is not a The electrostatic force F : field E : has the direction o opposite direction if q is n (A) 2 N/C (B) 50 N/C (C) 200 N/C P 1 Oil spray P 2 (D) cannot be determined Oil drop S A + B Insulating chamber wall Fig The Millikan oil-drop apparatus for measuring the elementary charge e.when a charged oil drop drifted into chamber C through the hole in plate P 1,its motion could be controlled by closing and opening switch S and thereby setting up or C Microscope Measuring the Eleme Equation played a American physicist Robe tation of his apparatus. W them become charged, e drop that drifts downwar Let us assume that this dr If switch S in Fig. 22- chamber C. If the switch positive terminal of the positive charge on condu ing plate P 2.The charge chamber C. According to charged drop that happe ular, our negatively charg

32 Question In an experiment, a potential difference (voltage) of V = 10V is x supplied to a pair of conducting e plates separated by a distance d = 20 cm. What is the electric field strength between the plates? E field that other charges h not the field set up by t acting on the particle in particle or object is not a The electrostatic force F : field E : has the direction o opposite direction if q is n (A) 2 N/C (B) 50 N/C (C) 200 N/C P 1 Oil spray P 2 (D) cannot be determined Oil drop S A + B Insulating chamber wall Fig The Millikan oil-drop apparatus for measuring the elementary charge e.when a charged oil drop drifted into chamber C through the hole in plate P 1,its motion could be controlled by closing and opening switch S and thereby setting up or C Microscope Measuring the Eleme Equation played a American physicist Robe tation of his apparatus. W them become charged, e drop that drifts downwar Let us assume that this dr If switch S in Fig. 22- chamber C. If the switch positive terminal of the positive charge on condu ing plate P 2.The charge chamber C. According to charged drop that happe ular, our negatively charg

33 Milikan s Oil Drop Experiment

34 S v Milikan s T under the influence of the Oil Drop Experiment demonstrated the qu gravitational and drag forces. gravitational, and drag forces. Figure 25.21, contain S S are allowed qe to pass t F D to ionize the air in t S drops, giving them a v T illuminate the S S E oil dro v q perpendicular T to the as shining stars again fall can be determine mg S Let s assume S a sin mg a viewed S F D and its charge F D v T, w is weight of droplet b ( the two forces acting v ) When the electric field qe is turned = w + Figure w T ward and The forces a viscous acting d v T on a negatively drag force charged is oil proporti drop- on, the droplet moves upward at S influence of the electric,

35 Milikan s Oil Drop Experiment Conclusion: all drops had a charge that was some number of multiples of e. Accepted value: q = ne ; n Z e = (35) C Millikan s value: e = (17) C A bit low...

36 Milikan s Oil Drop Experiment Richard Feynman: Millikan measured the charge on an electron by an experiment with falling oil drops, and got an answer which we now know not to be quite right. It s a little bit off because he had the incorrect value for the viscosity of air. It s interesting to look at the history of measurements of the charge of an electron, after Millikan. If you plot them as a function of time, you find that one is a little bit bigger than Millikan s, and the next one s a little bit bigger than that, and the next one s a little bit bigger than that, until finally they settle down to a number which is higher. Why didn t they discover the new number was higher right away?... When they got a number that was too high above Millikan s, they thought something must be wrong and they would look for and find a reason why something might be wrong. When they got a number close to Millikan s value they didn t look so hard.

37 Summary conductor in an electric field dipole in an electric field Millikan s experiment Homework Study for test tomorrow. Serway & Jewett: Ch 25, Problems: 49, 51