Two circular discs spaced apart from a parallel plate capacitor ?

[Netsurfer733]

Homework Statement

Two circular disks spaced 0.50 mm apart from a parallel-plate capacitor. Transferring 1.90 x 10^9 electrons from one disk to the other causes the electric field strength to be 1.90 x 10^5 N/C. What are the diameters of the disks (in cm)?

Homework Equations

E = Q / (e_o * A)
A = [pie]*r^2

The Attempt at a Solution

I though I went through the right process for this, but maybe I'm not using the right equations somehow? Here's what I did:

E = Q / (e_o * A) ==> Q = (8.85*10^-12 C^2 / N*m^2) * A * (1.9*10^5 N/C) = 3.04 * 10^-1

A = [Pie]*r^2 ==> 1.81 * 10^-4 = [pie]*r^2 ==> r = 0.00759 and thusly D = 0.1517m which is equal to 15.2 cm. This turned out to be wrong.

Where did I mess up?

 

[gneill]

Your derivation is a bit confusing; you seem to be mixing in pre-calculated values without showing how you got them. For example, I assume that the value "3.04 * 10^-1" is supposed to be the charge due to the moved electrons. The mantissa looks okay, but the power of ten is way off. Perhaps your value for A is off because of that.

 

[eczeno]

well, the first thing i see is that your diameter is more than twice your radius.

the first line of your solution is confusing; it looks like you are doing many steps at once and i am not sure what the last number is supposed to be since there are no units (if it is supposed to be the charge, it seems too big).

the reasoning is correct as far as i can tell, but you need to check your arithmetic and the value of the charge.

 

[Netsurfer733]

well, the first thing i see is that your diameter is more than twice your radius.

D'oh! That was it! Hahah - thanks much, and sorry for the confusion :) You just allowed me to pass this assignment ^.^

 

[rwisz]

Your calculations are correct, but you have made a mistake in converting the units. The given distance between the disks is 0.50 mm, which is equal to 0.005 m. Your answer for the diameter is in meters, but the question asks for it in centimeters. Therefore, the correct answer is 15.17 cm. It is always important to pay attention to units and make sure they are consistent throughout the calculation.