Electricity and Magnetism Electric Field

Transcription

1 Electricity and Magnetism Electric Field Lana Sheridan De Anza College Jan 11, 2018

2 Last time Coulomb s Law force from many charges

3 R/2 +8Q Warm Up Question (c) articles. p Fig Question In Fig , a central particle of charge 2q is surrounded by a square array of charged particles, separated by either distance d or d/2 along the perimeter of the square. What are the magnitude and direction of the net electrostatic force on the central particle due to the other particles? (Hint: Consideration of symmetry can greatly reduce the amount of work required here.) d +2q 7q +4q e 5q 3q e +3q 2q d 3q 5q e +4q 7q +2q Fig Question 10.

4 Overview forces at a fundamental level electric field field from many charges electric field lines net electric field

5 Forces at a Fundamental Level Often people think about two kinds of forces: contact forces and field forces (ie. forces that act at a distance). In mechanics problems, all forces except gravity are from direct contact. Gravity is a field force. The electric and magnetic forces are also field forces.

6 Forces at a Fundamental Level Often people think about two kinds of forces: contact forces and field forces (ie. forces that act at a distance). In mechanics problems, all forces except gravity are from direct contact. Gravity is a field force. The electric and magnetic forces are also field forces. And actually, at a fundamental level, all forces that we know of are field forces.

7 Forces at a Fundamental Level Contact forces are a result of electrostatic repulsion at very small scales.

8 Forces at a Fundamental Level Contact forces are a result of electrostatic repulsion at very small scales. Fundamental forces: Force Rel. strength Range (m) Attract/Repel Carrier Gravitational attractive graviton Electromagnetic 10 2 attr. & rep. photon Weak Nuclear < attr. & rep. W +, W, Z 0 Strong Nuclear 1 < attr. & rep. gluons

9 Forces at a Fundamental Level Contact forces are a result of electrostatic repulsion at very small scales. Fundamental forces: Force Rel. strength Range (m) Attract/Repel Carrier Gravitational attractive graviton Electromagnetic 10 2 attr. & rep. photon Weak Nuclear < attr. & rep. W +, W, Z 0 Strong Nuclear 1 < attr. & rep. gluons

10 Forces at a Fundamental Level Contact forces are a result of electrostatic repulsion at very small scales. Fundamental forces: Force Rel. strength Range (m) Attract/Repel Carrier Gravitational attractive graviton Electromagnetic 10 2 attr. & rep. photon Weak Nuclear < attr. & rep. W +, W, Z 0 Strong Nuclear 1 < attr. & rep. gluons Gravity is actually quite a weak force, but it is the only one that (typically) matters on large scales - charges cancel out!

11 Fields field (physics) A field is any kind of physical quantity that has values specified at every point in space and time.

12 Vector Fields In EM we have vector fields. The electrostatic force is mediated by a vector field. vector field (physics) any kind of physical quantity that has values specified as vectors at every point in space and time. vector field (math, 3 dimensions) A vector field is a vector-valued function F that takes a point (x, y, z) and maps it to a vector F(x, y, z).

13 Fields Fields were first introduced as a calculation tool. A force-field can be used to identify the force a particular particle will feel at a certain point in space and time without needing a detailed description of the other objects in its environment that it will interact with.

14 Fields Fields were first introduced as a calculation tool. A force-field can be used to identify the force a particular particle will feel at a certain point in space and time without needing a detailed description of the other objects in its environment that it will interact with. Imagine a charge q 0. We want to know the force it would feel if we put it at a specific location.

15 Fields Imagine a charge q 0. We want to know the force it would feel if we put it at a specific location. The electric field E at that point will tell us that! F = q 0 E Charges (source of E-field) Environment Field System +q F E Charges (source of E-field)

16 Fields Charges (source of E-field) Environment Field System +q F E Charges (source of E-field) The source of the field could be another charge or charges, but we do not need a description of the sources of the field to describe what their effect is on our particle. All we need to know is the field! (This is also true for gravity. We do not need the mass of the Earth to know something s weight: F G = m 0 g.)

17 Vector Fields 2 - dimensional examples Irrotational (curl-free) field.

18 Vector Fields 2 - dimensional examples Solenoidal (divergence-free) field.

19 22 Force from an Electic Field F (a) Test charge q 0 at point P but also: E Charged object The rod sets up F an = q 0 E electric field, which can create a force on the test charge. E = F q 0 1 Figure from P Halliday, Resnick, Walker. ) E 22-1 WHAT IS The force on a particle 1 of c P + physics charge q A nagging q ence of + particle + 2? Tha 2push + + on particle 1 ho One purpose of phy magnitude and direction deeper explanation of w such a deeper explanati tance. We can answer th field in the space surroun space, the particle know Electric field at point P can create a forc on the test charg

20 E-Field from a Point Charge We want an expression for the electric field from a point charge, q. Using Coulomb s Law the force on the test particle is F 0 = k qq 0ˆr. r 2 E = F ( ) 1 k q q 0 = q 0 q 0 r 2 ˆr The field at a displacement r from a charge q is: E = k q r 2 ˆr

21 tract each other.the pattern of field lines and the electric field it represents have rotational symmetry about an axis passing through both The field at a displacement charges in the plane r from of the a page.the charge qelectric is: field vector at one point E = k is q shown; the vector is tangent to the field line through r 2 ˆr the point. Field from a Point Charge This is a vector field: + toward the point c The direction of directly away fro Because the gives the field at point charge is sh We can quick charge. If we plac from Eq. 21-7, the Therefore, from Fig The electric field vectors at Here E : i is the el Equation 22-4 s

22 Field Lines Fields are drawn with lines showing the direction of force that a test particle will feel at that point. The density of the lines at that PART 3 point in the diagram indicates the approximate magnitude of the 581 force at that point ELECTRIC FIELD LINES e the electric field of a charged charge. The field at point P in t charge of Fig. 22-1a was put the presence of the test charge rged object, and thus does not interaction between charged tric field produced by a given e that a given field exerts on a ections 22-4 through 22-7 for nd task in Sections 22-8 and int charges in an electric field. c fields. tric fields in the 19th century, d with lines of force. Although ow usually called electric field rns in electric fields. Electric field lines F + Positive test charge (a) E (b)

23 Field from many charges The field is just the force divide by the charge. So, what is the force from many charges?

24 Field from many charges The field is just the force divide by the charge. So, what is the force from many charges? F net! F net,0 = F F F n 0

25 Field from many charges The field is just the force divide by the charge. So, what is the force from many charges? F net! F net,0 = F F F n 0 E net = F net q 0 Total electric field: E net = E 1 + E E n

26 Question about field from point charges 22-4 THE ELECTRIC FIELD DUE TO A POINT C Consider a proton p and an electron e on an x axis. x S e R p on p and an electron e on on of the electric field due to the electron at (a) point S and ction of What the net iselectric the direction field at (c) of point the electric R and (d) field point due S? to the electron only at point S and point R? (A) leftward at S, leftward at R Sample Problem (B) leftward at S, rightward at R Net electric field due to three charged particles (C) rightward at S, leftward at R particles (D) with rightward charges at qs, 1 2Q, rightward at R E each a distance d from the origin Q 4 0 d and E produced at the origin? We next must find the orientations o 1 Figure from Halliday, Resnick, Walker, field page vectors 583. at the origin. Because q 1 is

27 Question about field from point charges 22-4 THE ELECTRIC FIELD DUE TO A POINT C Consider a proton p and an electron e on an x axis. x S e R p on p and an electron e on on of the electric field due to the electron at (a) point S and ction of What the net iselectric the direction field at (c) of point the electric R and (d) field point due S? to the electron only at point S and point R? (A) leftward at S, leftward at R Sample Problem (B) leftward at S, rightward at R Net electric field due to three charged particles (C) rightward at S, leftward at R particles (D) with rightward charges at qs, 1 2Q, rightward at R E each a distance d from the origin Q 4 0 d and E produced at the origin? We next must find the orientations o 1 Figure from Halliday, Resnick, Walker, field page vectors 583. at the origin. Because q 1 is

28 Question about field from point charges 22-4 THE ELECTRIC FIELD DUE TO A POINT C Consider a proton p and an electron e on an x axis. x S e R p on p and an electron e on on of the electric field due to the electron at (a) point S and ction of What the net iselectric the direction field at (c) of point the net R and electric (d) point field S? at point S and point R? (A) leftward at S, leftward at R Sample Problem (B) leftward at S, rightward at R Net electric field due to three charged particles (C) rightward at S, leftward at R particles (D) with rightward charges at qs, 1 2Q, rightward at R E each a distance d from the origin Q 4 0 d and E produced at the origin? We next must find the orientations o 1 Figure from Halliday, Resnick, Walker, field page vectors 583. at the origin. Because q 1 is

29 Question about field from point charges 22-4 THE ELECTRIC FIELD DUE TO A POINT C Consider a proton p and an electron e on an x axis. x S e R p on p and an electron e on on of the electric field due to the electron at (a) point S and ction of What the net iselectric the direction field at (c) of point the net R and electric (d) point field S? at point S and point R? (A) leftward at S, leftward at R Sample Problem (B) leftward at S, rightward at R Net electric field due to three charged particles (C) rightward at S, leftward at R particles (D) with rightward charges at qs, 1 2Q, rightward at R E each a distance d from the origin Q 4 0 d and E produced at the origin? We next must find the orientations o 1 Figure from Halliday, Resnick, Walker, field page vectors 583. at the origin. Because q 1 is

30 Field Lines metric electric An electric field produced by an a point The charge electrostatic field electric caused dipole by an electric dipole system looks something like: Notice that the lines c point outward from a positive charge and inward toward a negative charge. are intersections of these surfaces with the page) and elecendicular 1 to Figure the electric from Serway field & lines Jewett at every point.

31 Summary vector fields electric field field of a point charge net field Homework Collected homework 1, posted online, due on Monday, Jan 22. Serway & Jewett: Read Ch 23 Ch 23, onward from page 716. Section Qs: 23, 33, 47, 49