Electricity and Magnetism

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Presentation transcript:

Electricity and Magnetism Physics 208 Dr. Tatiana Erukhimova Lecture 9

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

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.

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

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 .

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.

Flux of electric field S S

The flux of

More on area vector …. n

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 ?

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?

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?

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 .

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

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