Download presentation

Presentation is loading. Please wait.

Published bySally Ormes Modified over 3 years ago

1
METHOD OF IMAGES

2
Class Activities: Method of Images

3
Whiteboard: Calculate voltage (everywhere in space!) for 2 equal/opposite point charges a distance “d” above and below the origin. Where is V(r)=0?

4
A) Simple Coulomb’s law: B) Something more complicated A point charge +Q sits above a very large grounded conducting slab. What is E(r) for other points above the slab? z x y +Q 3.7 r

5
Infinite grounded conducting slab

6
Boundary Conditions: (grounded)

7
Calculate voltage V(r) (everywhere in space!) for 2 equal/opposite point charges a distance “d” above and below the origin. Where is V(r)=0? (If you’re done early, figure out Ex, Ey, and Ez from this voltage, and evaluate (simplify) AT the plane z=0)

8
Boundary Conditions: (grounded)

9
Boundary Conditions: “Image Charge” (grounded)

11
Method of Images Last Class: Uniqueness Theorem If: & & If: on the boundaries Poisson’s Equation Then:everywhere (within the boundaries)

12
Boundary Conditions: Uniqueness Theorem (grounded)

13
Siméon Denis Poisson 1781-1840 Method of Images

14
William Thomson (Lord Kelvin) 1824-1907 Method of Images

15
James Clerk Maxwell 1831-1879 “Treatise on Electricity and Magnetism” 1873, Vol. 1, Ch. XI (p. 245-283, 3 rd Ed.) Method of Images

16
Boundary Conditions: (grounded)

17
Boundary Conditions: (grounded)

18
A) 0 B) C) D) Something more complicated A point charge +Q sits above a very large grounded conducting slab. What is the electric force on this charge? z x y +Q d 3.8

19
A) B) Something else. A point charge +Q sits above a very large grounded conducting slab. What's the energy of this system? +Q 3.8b z x y d

21
3.9 Two ∞ grounded conducting slabs meet at right angles. How many image charges are needed to solve for V(r)? +Q A) one B) two C) three D) more than three E) Method of images won't work here r

22
On paper (don’t forget your name!) in your own words (by yourself): What is the idea behind the method of images? What does it accomplish? What is its relation to the uniqueness theorem?

23
Could we use the method of images for THIS problem? Find V(r) everywhere z>0, Given these two charges above a (grounded, infinite, conducting) plane? A)Yes, it requires 1 “image charge” B)Yes, it requires 2 images C)Yes, more than 2 image charge D) No, this problem can NOT be solved using the “trick” of image charges…

24
Could we use the method of images for THIS problem? Find V(r) everywhere z>0, Given these two charges above a (grounded, infinite, conducting) plane?

Similar presentations

Presentation is loading. Please wait....

OK

Sec. 5.5 Law of sines.

Sec. 5.5 Law of sines.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on product specification definition Ppt on potential reuse of plastic waste in road construction Ppt on trial balance sheet 5s presentation free download ppt on pollution Ppt on dining etiquette Ppt on human resource department Ppt on microsoft word 2003 7 segment led display ppt on ipad Ppt on new technology in mechanical Ppt on hdfc mutual fund