Solving Gauss' Law: E Field & Volume Charge Density

[suspenc3]

Homework Statement

1.)Two large metal plates of area $$1.0m^2$$ face each other. They are 5 cm apart and have equal but opposite charges on their inner surfaces. If the magnitude E of the electric field between the plates is 55N/C, what is the magnitude of the charge on each plate?Neglect edge effects

2.)A non conducting sphere has a uniform volume charge density $$\rho$$. Let r be the vector from the center of the sphere to a general point P within the sphere. Show that the electric field at P is given by $$E=\rho r/3\epsilon_0$$

Homework Equations

$$E=\sigma/\epsilon_0$$

The Attempt at a Solution

1.)$$E=\sigma/\epsilon_0$$
$$E\epsilon_0=\sigma=(55N/c)(8.85x10^{-12}F/m)=4.868x10^{-10}C/m^2$$
$$E=\sigma/2\epsilon_0=\frac{4.868x10^{-10}C/m^2}{2(8.85x10^{-12}F/m} = 27.5N/C$$

Im guessing that I did this wrong, it seemed too easy.

2.)I don't know how to start this one.

 

[Saketh]

For the second problem, just use Gauss's law.

$$\int_S \vec{E} \cdot \, \vec{dA} = \frac{q}{\epsilon_0}$$

The important thing is to be careful in selecting your surfaces. Here's a suggestion -- use a Gaussian surface that is a spherical shell concentric with the sphere itself.

So the left side simplifies essentially to EA, where A is just $4\pi r^2$, where A is the surface area of our Gaussian surface (r < R).

Now, how do you find q? That is, how do you find the charge enclosed by our Gaussian surface? (I'll leave this part to you.)