How to Solve a Gauss' Law Problem in a Spherical Region?

[dpd069]

Homework Statement

In a spherical region, the voltage is measured to be spherically symmetrical, with v=v(r)=wr^p
a. Find the radial electric field.
b. Use Gauss’ Law to find the charge enclosed in a sphere of radius r.
c. Find the charge enclosed by a sphere of radius r+dr.
d. Find the differential charge enclosed in the annular region between two concentric spheres of radii r and r+dr.
e. Find the differential volume of the annular region between two concentric spheres of radii r and r+dr.
f. Find the charge density, rho=rho(r)=?

Homework Equations

The Attempt at a Solution

i am pretty sure that part a would be v(r)= - integral E(r) dr. so the radial electric field would be -Pwr^(p-1)

i am confused on how to do the rest. any help/hints would be appreciated.

 

[Feldoh]

Well what does gauss' law state?

 

[dpd069]

Gauss' law states that the flux of the electric field is equal to Q/epsilon0.

my question then is how do i relate that to the given statement v(r)=wr^p?