1. Electricity and Magnetism
Physics 208
Dr. Tatiana Erukhimova
Lecture 9

2. For a point charge at the origin:

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

4. 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?

5. 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?

6. 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?

7. 2D case:

8. 2 or 3D cases: If or
then

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

10. 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

11. 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.

12. 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?

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