Electricity and Magnetism Physics 208 Dr. Tatiana Erukhimova Lecture 8

P218 Review: Conservative forces One-dimensional problem:

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

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

For a point charge at the origin:

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?

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?

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?

2D case:

2 or 3D cases: If or then

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

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

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