2. A charged particle with positive charge q 1 is fixed at the point x=a, y=b. What are the x and y components of the force on a particle with positive charge q 2 which is fixed at the point x=c, y=d? Quiz y x q1q1 q2q2

5. The negative charge of electron has exactly the same magnitude as the positive charge of the proton. Neutral atom Positive ion Negative ion

6. Charging of neutral objects 1) By contact: 2) By induction (we’ll talk about it a little bit later) a) b)

7. How you can make a balloon stick to the wall?

8. Principle of Superposition (revisited) The presence of other charges does not change the force exerted by point charges. One can obtain the total force by adding or superimposing the forces exerted by each particle separately. Suppose we have a number N of charges scattered in some region. We want to calculate the force that all of these charges exert on some test charge.

9. We introduce the charge density or charge per unit volume How do we calculate the total force acting on the test charge ?

10. We chop the blob up into little chunks of volume ; each chunk contains charge. Suppose there are N chunks, and we label each of them with some index. Let be the unit vector pointing from th chunk to the test charge; let be the distance between chunk and test charge. The total force acting on the test charge is This is approximation!

11. The approximation becomes exact if we let the number of chunks go to infinity and the volume of each chunk go to zero – the sum then becomes an integral: If the charge is smeared over a surface, then we integrate a surface charge density over the area of the surface A: If the charge is smeared over a line, then we integrate a line charge density over the area of the length:

12. Problem 6 page 10 Suppose a charge were fixed at the origin and an amount of charge Q were uniformly distributed along the x-axis from x=a to x=a+L. What would be the force on the charge at the origin?

13. Another example on force due to a uniform line charge A rod of length L has a total charge Q smeared uniformly over it. A test charge q is a distance a away from the rod’s midpoint. What is the force that the rod exerts on the test charge?

14. The electric field y x has the same direction as

15. Michael Faraday 1791-1867 “The best experimentalist in the history of science”

16. Electric field lines These are fictitious lines we sketch which point in the direction of the electric field. 1) The direction of at any point is tangent to the line of force at that point. 2) The density of lines of force in any region is proportional to the magnitude of in that region Lines never cross.

19. Have a great day! Please don’t forget your pictures Hw: All Chapter 1 problems and exercises Reading: Chapter 2