# Gauss's Law, Sphere (Electric Field

## Homework Statement

See figure attached.

## The Attempt at a Solution

I'm extremely confused.

For r<1,

The total charge enclosed should always be,

$\rho \frac{4}{3\epsilon_{0} \epsilon_{r}} \pi r^{3} = \oint _{S} \vec{E} \cdot \vec{dA} = I$

The electric field will disperse radially out of the sphere, in the same direction as $\vec{dA}$ so,

$I = E\oint_{S} dA = 4\pi r^{2}E$

Thus,

$E = \frac{\rho r}{3 \epsilon_{0} \epsilon_{r}}$

I'm confused about what is suppose to change in the region r > 1 ?

Can someone explain?

#### Attachments

• QQZ2010.JPG
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