1. Electricity and Magnetism
Physics 208
Dr. Tatiana Erukhimova
Lecture 10

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

3. Electric field lines
These are fictitious lines we sketch which point in the direction of the electric field.
1) The direction of at any point is tangent to the line of force at that point.
2) The density of lines of force in any region is proportional to the magnitude of in that region
Lines never cross.

4. Density is the number of lines going through an area (N) divided by the size of the area
For a charge q located at the origin
It is important that the force is proportional to

5. 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

6. What is or flux of any vector, e.g. velocity of a water flow?
Consider a flow with a velocity vector
Let S be a small area perpendicular to
Area vector
b) Now S is tilted with respect to The volume of water flowing through S per unit time is n S b) S
Flux: a)
a) The volume of water flowing through S per unit time is
is the angle between velocity vector and unit vector normal to the surface S.

7. Flux of electric field S S

8. The flux of

9. More on area vector …. n

10. Suppose there was an electric field given by
What would be the electric flux through a plane with area A if the plane were oriented in the y-z plane at ?
What would be the electric flux if the plane were oriented in the x-z plane at ?

11. Quiz Suppose there was an electric field given by
What would be the electric flux through a plane with area A if the plane were oriented in the xz plane at y = y0?
What would be the electric flux if the plane were oriented in the yz plane at x = x0?

12. Quiz Suppose there was an electric field given by
What would be the electric flux through a front side of a cube of side L?

13. 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

14. S Definition of a solid angle does not depend on radius The largest
Then

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