# What is the surface charge density on the face of the penny?

1. Feb 15, 2017

### Mason Smith

1. The problem statement, all variables and given/known data
The electric field strength just above one face of a copper penny is 2230 N/C. What is the surface charge density on this face of the penny?

2. Relevant equations
Electric field of an infinite plane of charge = η/(2*ε0)

3. The attempt at a solution
I used the above equation, and the result was 3.95 x 10-8C/m2. However, this is not the correct answer. Where am I going wrong in my thinking? This homework problem comes from the textbook chapter about Gauss's Law, yet I do not see how Gauss's Law can tie into this question.

2. May 7, 2017

### Mason Smith

To anyone who needs help with this problem, I believe that I have found a solution.
The equation for surface charge density is η = Q/A. Since the electric field is just above the face of the penny, the penny can be modeled as an infinite plane of charge Eplane = η/(2ε0). Combining these equations will result in Eplane = Q/(A⋅2⋅ε0). Rearranging this equation to find the surface charge density will be (Q/A) = (Eplane⋅2⋅ε0). However, this will be the surface charge density for both sides of the penny. In order to find the surface charge density of only one side of the penny, divide Eplane⋅2⋅ε0 by 2.

3. May 8, 2017

### kuruman

You didvide by 2 too many times. If η is the surface charge density on one side, and you construct the standard Gaussian pillbox sticking out both sides of the penny, then the total electric flux through the pillbox is ΦE = 2EpaneA. The total charge enclosed is Qencl. = 2ηA (ηA per side).
By Gauss's law, 2EplaneA = 2ηA/ε0 which gives η = ε0Eplane.