Electricity and Magnetism Motion of a Charge in an E-field

Transcription

1 Electricity and Magnetism Motion of a Charge in an E-field Lana Sheridan De Anza College Oct 1, 2015

2 Last time E-field from many charges electric fields of charge distribution

3 Overview motion of charges in electric fields

4 nes, they still provide a nice way to visualize patterns in electric fields. The relation between the field lines and electric field vectors is this: (1) At ny point, the direction of a straight field line or the direction of the tangent to a F Electric field due to an Infinite : acting on a positive test charge near a E at that point, and (2) the field lines are Sheet of Charge : sphere of uniform negative charge. (b) rved field line gives the direction of rawn so that the number of lines per unit area, measured in a plane that is erpendicular to the lines, is proportional to the magnitude of E :. Thus, E is large here field lines are close together and small where they are far apart. Figure 22-2a shows a sphere of uniform negative charge. If we place a positive st charge anywhere near the sphere, an electrostatic force pointing toward the nter of the sphere will act on the test charge as shown. In other words, the elecic field vectors at all points near the sphere are directed radially toward the here. This pattern of vectors is neatly displayed by the field lines in Fig. 22-2b, hich point in the same directions as the force and field vectors. Moreover, the The field lines extend toward the negatively and charged the sphere. charge (They originate density on Suppose the sheet is in air (or vacuum) on distant positive charges.) the sheet is σ (charge per unit area): E = σ 2ɛ 0 reading of the field lines with distance from the sphere tells us that the magnide of the electric field decreases with distance from the sphere. If the sphere of Fig were of uniform positive charge, the electric field ectors at all points near the sphere would be directed radially away from e sphere. Thus, the electric field lines would also extend radially away from the here.we then have the following rule: Fig (a) The electrostatic force The electric field vector E : at the location of the test charge, and the electric field lines in the space near the sphere. It is uniform! It does not matter how far a point P is from the sheet, the field is the same. Electric field lines extend away from positive charge (where they originate) and toward negative charge (where they terminate). Figure 22-3a shows part of an infinitely large, nonconducting sheet (or plane) ith a uniform distribution of positive charge on one side. If we were to place a ig (a) The electrostatic force on a positive test charge near a very rge, nonconducting sheet with unirmly distributed positive charge on ne side. (b) The electric field vector E : t the location of the test charge, and e electric field lines in the space ear the sheet.the field lines extend way from the positively charged eet. (c) Side view of (b). (a) Positive test charge F (b) E (c)

5 Field Lines: Uniform Field The field from two infinite charged plates is the sum of each field. E = σ ɛ 0 s P 0 (24.8) 14 (Example 24.5) Figure (Example 24.5) The field in the center of a parallel plate capacitor is nearly uniform.

6 ing plate P 2 e.when a charged oil drop drifted into chamber C. chamber C through the hole in plate P 1,its charged dro The force on motion a charged could particle be controlled is givenby byclosing F = qe. and ular, our ne opening switch S and thereby setting up or If the charge eliminating is free to an move, electric it will field accelerate in chamber in the C. direction of By timi the force. The microscope was used to view the drop, and thus de to permit timing of its motion. values of q w Example: Ink-jet printing Free charges in an E-field Input signals E Deflecting plate in which e charge, 1.60 quantized, a Modern me experiment G C Fig Deflecting plate Ink-jet printer. Drops shot Ink-Jet Pri The need alternative

7 oblem Motion of a Charged Particle in an E-field le in an electric field If Q is negative: y Plate 0 E Plate m,q x = L x ig An ink drop of mass m and charge magnitude Q i eflected in the electric field of an ink-jet printer.

8 oblem Motion of a Charged Particle in an E-field le in an electric field If Q is negative: y Plate 0 E Plate m,q x = L x ig An ink drop of mass m and charge magnitude Q i Trajectory is a parabola: similar to projectile motion. eflected in the electric field of an ink-jet printer.

9 The electron undergoes a downward Motion of a Charged ParticleS in an E-field as shown acceleration (opposite E), and its motion N/C. The (a) What is the acceleration is parabolic while of an it is electron between the in the plates. field of strength E? he elecding one y perpenthe veloctric field a curved lectron is tally in a v i î (0, 0) S E ecause the electric field is uniform, a constant electric force is electron, we can model it as a particle under a net force. (x,y) Figure (Example 23.11) An electron is projected horizontally leaves theinto field a uniform at the point electric (l, field y f ). pro- What is y f in (b) The charge terms of duced l, v by two charged plates. i, E, e, and m e? y v S x

10 The electron undergoes a downward Motion of a Charged ParticleS in an E-field as shown acceleration (opposite E), and its motion N/C. The (a) What is the acceleration is parabolic while of an it is electron between the in the plates. field of strength E? he elecding one y perpenthe veloctric field a curved lectron is tally in a v i î (0, 0) S E Figure (Example 23.11) An electron is projected horizontally leaves theinto field a uniform at the point electric (l, field y f ). pro- What is y f in (b) The charge terms of duced l, v by two charged plates. i, E, e, and m e? ecause the electric field is uniform, y f = a constant eel2 2m electric force is e vi 2 electron, we can model it as a particle under a net force. (x,y) y v S x

11 Millikan s Oil Drop Experiment: Measuring e The e field E : opposi P 1 Fig Oil spray Oil drop P 2 S A C B Insulating chamber wall Microscope The Millikan oil-drop appa- Measu Equatio Americ tation o them be drop th Let us a If s chambe positive positive

12 Sparking: Electrical Breakdown Electric fields can cause forces on charges. If the field is very strong, it begins to accelerate free electrons which strike atoms, knocking away more electrons forming ions. This starts a cascade, forming a spark.

13 Sparking: Electrical Breakdown Electric fields can cause forces on charges. If the field is very strong, it begins to accelerate free electrons which strike atoms, knocking away more electrons forming ions. This starts a cascade, forming a spark. The strength of the field where this happens is called the critical field, E c, For air E c N/C.

14 Sparking: Electrical Breakdown Electric fields can cause forces on charges. If the field is very strong, it begins to accelerate free electrons which strike atoms, knocking away more electrons forming ions. This starts a cascade, forming a spark. The strength of the field where this happens is called the critical field, E c, For air E c N/C. The air along the spark becomes a plamsa of free charges and can conduct electricity. Sparks look like bright streaks because the air molecules becomes so hot. Accelerating charges radiate, so lightning can also cause radio interference.

15 Question Page 597, #1 1 Figure shows three arrangements of electric field lines. In each arrangement, a proton is released from rest at point A and is then accelerated through point B by the electric field. Points A and B have equal separations in the three arrangements. Rank the arrangements according to the linear momentum of the proton at point B,greatest first. A B A B A B (a) (b) (c) Fig Question 1. ducin the n the su two 2E)? those cel? add o of the celing rectio 4 Fi cles a charg magn

16 E : ctric field of the, we For considered next time: the Gauss s Law basic idea Then we simplified dicular Gauss s components law relates the electric field across a closed surface (eg. a sphere) to the amount of net charge enclosed by the surface. save far more work matician and physing the fields de : Spherical of Gaussian siders a hypothetical surface is Gaussian surface, s our calculations of distribution. For exse the sphere with a en, as we discuss in t that? ian surface to the E field on a Gaussian Fig A spherical Gaussian s a limited example, surface. If the electric field vectors lly outward Can from we quantify the the electric field across a boundary? are of uniform magnitude and point ediately tells us that radially outward at all surface points,

17 Summary motion of charges in E-fields Homework Halliday, Resnick, Walker: Read up through Chapter 23. Ch 22, onward from page 597. Problems: 39, 43