1. Electricity and Magnetism
Physics 208
Dr. Tatiana Erukhimova
Lecture 8

2. P218 Review: Conservative forces
One-dimensional problem:

3. Two-dimensional problem:
does NOT depend on path!
around the closed path is zero!

4. Chapter 3. Electric Potential
Constant electric field
The Electric Potential: V
- Single Charge
- Dipole
- conservative? potential energy function?

5. For a point charge at the origin:

6. There is an electric field given by
Ch3 Quiz 1
There is an electric field given by
where E0 is a constant.
What is the difference in the value of the electric potential due to this electric field between the origin and the point x=a, y=b?

7. There is an electric field given by
Ch3 Quiz 2
There is an electric field given by
where  and  are constants.
What is the difference in the value of the electric potential due to this electric field between the origin and the point x=a, y=b?

8. where c is a constant and r is the distance from the origin;
Ch3 Quiz 3
There is an electric field created by some source at the origin given by
where c is a constant and r is the distance from the origin;
points out from the origin.
What is the difference in the value of the electric potential due to this electric field between the point x=a, y=b and the point at infinity?
What is the potential function corresponding to this electric field if instead of being at the origin the source of the electric field is at point x=a, y=b?

9. 2D case:

10. 2 or 3D cases: If or
then

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

12. 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

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