EMT: 3rd week part 1 Electric Field Intensity of a finite and infinite surface of charges

By: Unknown on Monday, March 09, 2015

Hey there,

Today we learn about the Electric Field Intensity of a finite and infinite surface of charges. 

Coulomb's law still applied in this topic, but dQ will be different.    (2 variables). 

Since we already learn about Coulomb's law, lets straight get into one of the example to have a quick but better understanding on this.

Example:

A circular disk of radius a is uniformly charged with ps C/m2. If the disk lies on the z = 0 plane with its axis along the z-axis,

(a) Show that at point (0, 0, h)

(b) From this, derive the E field due to an infinite sheet of charge on the z = 0 plane.

Solution

(a)

The question stated that the unit of ps is C/m2, which means that it is a surface charges question. 

So the answer is already given, all we need to do is to prove it.

Please try to read the solution below carefully:

the only different here is dQ = rdrdphi. So, double integration is required to complete this question instead of only one integration needed when dealing with line charges.

Since we dealing with circular disc with constant density, we assume that vector r will eventually been all cancelled out, so only magnitude with z is existed.

(b) As a approaching infinity,  the equation we obtained in (a) can be further reduced.

Hope you guys can understand surface charges concept with this example!

See ya!