# Electric field between two plates

1. ### tag16

97
1. The problem statement, all variables and given/known data
Two 10 cm x 10cm square plates that are charged with ±12 nC and are 6 mm apart. What is the magnitude of the electric field between the two plates?

2. Relevant equations
E={sigma}{epsilon_0} .

3. The attempt at a solution

I know I have to use this equation but I'm not sure how to find the charge density. Also would it be E=sigma/2E_0 , since it's 2 plates or do I just plug the numbers into the formula?

2. ### TwoTruths

37
Assuming the plates are charged uniformly, the charge density is simply a direct application of its definition (charge per unit area). So, sigma = total charge / surface area of plate.

Note also that the distance between the two plates is very small compared to the size of the plates. I believe you can treat them as "infinitely" long plates, which will make the below physics easier.

Are you saying the plates are oppositely charged? Or are both - or both +?

Either way, consider the electric field lines of one plate. I will leave the general formula derivation for the electric field to you (hint: Gauss's Law). You should come up with a nice, simple formula.

Now, if we add a plate of opposite charge, what will happen to the field lines? You can see that the field lines outside of the plates disappears! Inside, the magnitude of the electric field will double. Nice, right?

If you add a plate of same charge, what will happen now? Basically the opposite, right? Inside, the two repulsion fields should cancel. Outside, the two repulsion forces should add up to double the original magnitude! Also nice!

Hope this helps!

((Easy way out: Calculate sigma and plug into your equation in section 2. I recommend doing the derivation as it's easy and will help you understand what's going on.))

Last edited: Sep 24, 2009
3. ### tag16

97
so would it just be (10x10)/10x10^-9 to get the charge density then divide that by E_0 to get the answer?

4. ### TwoTruths

37
Depends on the charge of the two plates. I'm assuming they're oppositely charged.

What you have ( $$\frac{10*10}{10*10^-9}$$ ) is not correct. I don't know where the denominator came from (enlighten?), but the numerator should be on the bottom. It's $$\frac{total charge}{total area}=\sigma$$.

Sorry, I just figured out this LaTeX thing, and it's pretty cool.

5. ### tag16

97
oh opps...it was suppose to 12x10^-9 which is the charge given in the problem