2. 2D case:

3. If or then 2 or 3D cases:

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

5. 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

6. 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.

7. 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?

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

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. Van de Graaff generator

14. Have a great day! Hw: All Chapter 3 problems and exercises Reading: Chapter 4