2. Problem 3 p. 45 Electric potential on ring’s axis From Chapter 2:

3. 2D case:

4. If or then 2 or 3D cases:

5. Several dimensions: U(x,y,z) Compact notation using vector del, or nabla: Another notation: Partial derivative is taken assuming all other arguments fixed

6. Geometric meaning of the gradient Direction of the steepest ascent; Magnitude : the slope in that direction Direction of the steepest descent Magnitude : the slope in that direction http://reynolds.asu.edu/topo_gallery/topo_gallery.htm

7. 1)The electric potential V in a region of space is given by where A is a constant. Derive an expression for the electric field at any point in this region. 2)The electric potential V in a region of space is given by where c is a constant. The source of the field is at the origin. Derive an expression for the electric field at any point in this region.

8. Exercise 5 p. 52 An electron moves from one point to another where the second point has a larger value of the electric potential by 5 volts. If the initial velocity was zero, how fast will the electron be going at the second point?

9. In electrostatics, the electric field is conservative: Chapter 3 Summary

10. In electrostatics: If we know V(x,y) we can find the components of electric field and

11. Electric potential V is a scalar!

12. An old rule of thumb: you have to study 2-3 hours a week outside the class per each credit hour

13. Outline Area vector Vector flux More problems Solid angle Proof of Gauss’s Law

14. Gauss’s Law The total flux of electric field out of any closed surface is equal to the charge contained inside the surface divided by.

15. Have a great day! Hw: All Chapter 4 problems and exercises Reading: Chapter 4