Gauss’s Law PH 203 Professor Lee Carkner Lecture 5

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

Gauss  F = q/  0  But the flux is related to the field through ∫EdA =q/  0   What surfaces will work?

Cylinder   We can capture the flux with a cylindrical Gaussian surface  What is ∫EdA ?   E constant everywhere   total charge is h   E = / (2  0 r)  Can sometimes use this to approximate a long thin charge distribution

Plane   We can again capture the flux with a cylindrical Gaussian surface  What is ∫EdA ?   E constant everywhere   total charge is  A   E =  /2  0  Useful for large sheet or point close to sheet

Spherical Shell  For a point charge surrounded by a sphere we found E = (1/4  0 )(q/r 2 )   Remember, only total q enclosed counts  What if we put the surface inside the charge?  E = 0

Surface within Sphere  What if we have total charge q, uniformly distributed with a radius R?   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

Van De Graaff Generator   The positively charged belt attracts the electrons in the dome making it positively charged  Belt moves electrons to a ground connection where they are dumped   Charge builds up until it is discharged through the air

Van De Graaff  Why does your hair stand up when you touch the Van De Graaff generator?   Why do you need to stand on the box? 

Conductors and Charge   The charges in the conductor are free to move and so will react to each other   Charge distributes itself over the surface of a conductor  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  For a non-uniform surface, charge accumulates at points 

Conductors and External  What if an external field is applied to a conductor?   A charge placed in the middle would feel a force from these charges equal and opposite to the external force, thus,  The field inside the conductor is zero  The charges in the conductor cancel out the external field 

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