Electric Field Models

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Preston Gilbert
5 years ago
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1 Electric Field Models One thing learned from last chapter was that sources determine the electric field. We can understand the essential physics on the basis of simplified models of the sources of electric field. Discrete sources of charge are straight forward but continuous charge is challenging. We will consider various geometries such as wires, rings, disk, and spheres. Slide 26-18

2 Electric Field of a Point Charge Slide 26-19

3 The Electric Field of Multiple Point Charges Suppose the source of an electric field is a group of point charges q 1, q 2, The net electric field E net at each point in space is a superposition of the electric fields due to each individual charge: Slide 26-21

4 Example 1 What is the strength of the electric field at the dot?

5 QuickCheck 26.1 What is the direction of the electric field at the dot? Slide 26-22

6 QuickCheck 26.2 What is the direction of the electric field at the dot? Slide 26-26

7 QuickCheck 26.3 When r d, the electric field strength at the dot is A. B. C. D. Slide 26-28

8 Electric Dipoles Two equal but opposite charges separated by a small distance form an electric dipole. The figure shows two examples. Slide 26-30

9 The Dipole Moment It is useful to define the dipole moment p, shown in the figure, as the vector: The SI units of the dipole moment are C m. Slide 26-31

10 The dipole electric field on axis Example 2 Find the electric field of an electric dipole on axis. Slide 26-32

The electric field in the plane that bisects and is perpendicular to the dipole is This

11 The Electric Field of a Dipole The electric field at a point on the axis of a dipole is: where r is the distance measured from the center of the dipole. The electric field in the plane that bisects and is perpendicular to the dipole is This field is opposite to the dipole direction, and it is only half the strength of the on-axis field at the same distance. Slide 26-33

12 Example 3 An ammonia molecule (NH 3 ) has a permanent electric dipole moment 5.0 x10-30 C m. A proton is 2.0 nm from the molecule in the plane that bisects the dipole. What is the electric force of the molecule on the proton?

13 The Electric Field of a Dipole This figure represents the electric field of a dipole as a fieldvector diagram. Slide 26-36

14 The Electric Field of a Dipole This figure represents the electric field of a dipole using electric field lines. Slide 26-37

15 Tactics: Drawing and Using Electric Field Lines Slide 26-35

16 The Electric Field of Two Equal Positive Charges This figure represents the electric field of two same-sign charges using electric field lines. Slide 26-38

17 QuickCheck 26.4 Two protons, A and B, are in an electric field. Which proton has the larger acceleration? A. Proton A. B. Proton B. C. Both have the same acceleration. Slide 26-39

18 QuickCheck 26.5 An electron is in the plane that bisects a dipole. What is the direction of the electric force on the electron? Slide 26-41

19 Continuous Charge Distributions The linear charge density of an object of length L and charge Q is defined as Linear charge density, which has units of C/m, is the amount of charge per meter of length. Slide 26-43

20 QuickCheck 26.6 If 8 nc of charge are placed on the square loop of wire, the linear charge density will be A. 800 nc/m. B. 200 nc/m. C. 8 nc/m. D. 2 nc/m. Slide 26-44

21 Continuous Charge Distributions The surface charge density of a twodimensional distribution of charge across a surface of area A is defined as: Surface charge density, with units C/m 2, is the amount of charge per square meter. Slide 26-46

22 A piece of plastic is uniformly charged with surface charge density 1. The plastic is then broken into a large piece with surface charge density 2 and a small piece with surface charge density 3. Rank in order, from largest to smallest, the surface charge densities 1 to 3. A. η 1 > η 2 > η 3 B. η 1 > η 2 = η 3 C. η 1 = η 2 = η 3 D. η 3 > η 2 > η 1

23 QuickCheck 26.7 A flat circular ring is made from a very thin sheet of metal. Charge Q is uniformly distributed over the ring. Assuming w R, the surface charge density is A. Q/2 Rw. B. Q/4 Rw. C. Q/ R 2. D. Q/2 R 2. E. Q/ Rw. Slide 26-47

24 Example 4 Find the electric field of a line of charge

25 An Infinite Line of Charge The electric field of a thin, uniformly charged rod may be written: If we now let L, the last term becomes simply 1 and we re left with: Slide 26-54

26 Example 5 Find the electric field of a line of charge

9/4/2018. Electric Field Models. Electric Field of a Point Charge. The Electric Field of Multiple Point Charges

9/4/2018. Electric Field Models. Electric Field of a Point Charge. The Electric Field of Multiple Point Charges Electric Field Models One thing learned from last chapter was that sources determine the electric field. We can understand the essential physics on the basis of simplified models of the sources of electric