Gauss’s Law PH 203 Professor Lee Carkner Lecture 5

Gauss   = q/  0 = ∫EdA  Note that:  Flux only depends on net q internal to surface   For a uniform surface and uniform q, E is the same everywhere on surface  so ∫EdA = EA

Cylinder   E field is always radially outward   We want to find E a distance r away  To solve Gauss’s Law:   = q/  0 = ∫EdA = EA  q is h   Solve for E a)

Plane   We can again capture the flux with a cylindrical Gaussian surface   Useful for large sheet or point close to sheet b)

Spherical Shell  Consider a spherical shell of charge of radius r and total charge q c) d)

Surface within Sphere  What if we have total charge q, uniformly distributed with a radius R? e)  What if surface is inside R?   If we apply r 3 /R 3 to the point charge formula we get, E = (q/4  0 R 3 )r

Conductors and Charge   The charges in the conductor are free to move and so will react to each other  Like charges will want to get as far away from each other as possible   No charge inside conductor

Charge Distribution  How does charge distribute itself over a surface?   e.g., a sphere   No component parallel to surface, or else the charges would move   Excess charge there may spark into the air

Conductors and External   The positive charges will go to the surface “upfield” and the negative will go to the surface “downfield”   The field inside the conductor is zero  The charges in the conductor cancel out the external field  A conductor shields the region inside of it

Conducting Ring Charges Pushed To Surface No E Field Inside Field Lines Perpendicular to Surface

Faraday Cage  If we make the conductor hollow we can sit inside it an be unaffected by external fields   Your car is a Faraday cage and is thus a good place to be in a thunderstorm 

Next Time  Read  Problems: Ch 23, P: 24, 36, 45, Ch 24, P: 2, 4

A uniform electric field of magnitude 1 N/C is pointing in the positive y direction. If the cube has sides of 1 meter, what is the flux through sides A, B, C? A)1, 0, 1 B)0, 0, 1 C)1, 0, 0 D)0, 0, 0 E)1, 1, 1 A B C

Consider three Gaussian surfaces. Surface 1 encloses a charge of +q, surface 2 encloses a charge of –q and surface 3 encloses both charges. Rank the 3 surfaces according to the flux, greatest first. A)1, 2, 3 B)1, 3, 2 C)2, 1, 3 D)2, 3, 1 E)3, 2, 1 +q-q 1 2 3

Rank the following Gaussian surfaces by the amount of flux that passes through them, greatest first (q is at the center of each). A)1, 2, 3 B)1, 3, 2 C)2, 1, 3 D)3, 2, 1 E)All tie qq 1 2 q 3

Rank the following Gaussian surfaces by the strength of the field at the surface at the point direction below q (where the numbers are). A)1, 2, 3 B)1, 3, 2 C)2, 1, 3 D)3, 2, 1 E)All tie qq 1 2 q 3