Calculating Electric Field of Spherical Charge Distribution

[tome101]

Homework Statement

Compute the electric field generated by a spherically symmetric charged sphere of radius R with charge density of $\rho = kr^{2}$

Homework Equations

$\oint _S \vec{E} \cdot \vec{dA} = \frac{Q_{enclosed}}{\epsilon_0}$

The Attempt at a Solution

I know that this question involves the application of Gauss' law but I don't really know how? To be honest I'm a bit sketchy on applying Gauss' law to any question. Any help would really be appreciated.

 

[ideasrule]

Imagine a Gaussian sphere of radius r, centered on the actual sphere of charge. What would the surface integral of E*dA be, in terms of r? Remember that due to symmetry, the electric field has to be constant for constant r, and must be entirely radial.

Using integration, can you also find Q_enclosed for this Gaussian sphere?

 

[tome101]

OK, by integration I've found the charge enclosed by the sphere to be (4pi*k*r^5)/5, but I'm not really sure where to go from here?

From
$\oint _S \vec{E} \cdot \vec{dA} = \frac{Q_{enclosed}}{\epsilon_0}$
I can see that I need to divide the charge enclosed by epsilon 0 then equate to the surface integral of E*da, but I'm not really sure how to calculate the surface integral of E*da?
Thanks

 

[tome101]

Ok, I've now been told that the surface integral of E*dA in this case goes to E(4pi*r^2) but I'm still not totally sure why.