What is the charge on a circular segment of a wide charged electrode?

[starrynight24]

Homework Statement

The electric field strength 5cm from a very wide charged electrode is 1000N/C. What is the charge (in nC) on a 1cm diameter circular segment of the electrode?

Homework Equations

E=Q/EoA

n=Q/A

3. The Attempt at a Solution [/b

I tried to figure out n, so that I can plug it into n=Q/A to figure out Q. But it didn't work.

 

[badphysicist]

Since the electrode is so wide compared to how far away the electric field is measured at, we may treat the electrode as an infinite insulating plane of charge for which the electric field is given by Gauss's Law. It yields $$E\equiv\frac{\sigma}{\epsilon_0}$$ where $$\sigma$$ is the area charge density of the plate. This is essentially what you had. You're given the electric field. Just make sure that when you calculate the area that you use the radius since you are given the diameter.

 

[starrynight24]

What equation do I need to use to apply the area and the electric field to get the charge? n=Q/A?

 

[badphysicist]

I'm not sure what your n is supposed to be.. Apparently is the area charge density which is conventionally denoted as $$\sigma$$. You are given the electric field so you can find the sigma and you also know the area so you can find the charge.

 

[Redbelly98]

Two symbols are being used for charge density here:

n = Q/A

$$\sigma$$ = Q/A