# Parallel plate capacitor and charge density

1. Mar 12, 2008

### tony873004

1. The problem statement, all variables and given/known data
A parallel plate capacitor with A=125 cm2 and d=1.25 mm is charged to a potential difference of 10.0 V. What is the charge density on each plate?

2. Relevant equations

$$V = \frac{{\sigma d}}{{\varepsilon _0 }}\,\,\,\, \Rightarrow \,\,\,\,V\varepsilon _0 = \sigma d\,\,\,\, \Rightarrow \,\,\,\,\sigma = \frac{{V\varepsilon _0 }}{d}$$

3. The attempt at a solution

Plugging in numbers, I get 8.5*10-8C/m2. But I never used the Area. My units seem to work. Did they throw in irrelavant data? Shouldn't I only need Area if I want total charge?

Should my answer be half of what I computed, because it is divided between 2 plates?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Mar 12, 2008

### Hootenanny

Staff Emeritus
As far as I'm concerned your solution is correct. As you correctly point out, one only needs the area to calculate the total charge on each plate. Further, you do not need to halve your answer since the surface charge density is calculated for each plate. You can check your solution by placing a Gaussian surface around one plate. Perhaps http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elesht.html#c2" would be helpful.

Last edited by a moderator: Apr 23, 2017
3. Mar 12, 2008

### tony873004

Thanks for the feedback and the link!