Find electric field strength expression for a specfic region

[jlmccart03]

Right. And similarly, the volume of a sphere of radius a is (4/3)πr³.

The sphere of radius a happens to be the volume of the empty cavity within the shell. So the volume of the shell from a out to r is equal to the volume of the solid sphere of radius r minus the volume of the sphere of radius a (you're removing the volume of the cavity from that of a solid sphere).

So ((4/3)π(r³-a³))/(4πε₀))ρ.

 

[gneill]

So ((4/3)π(r³-a³))/(4πε₀))ρ.

Close. You're missing the r² in the denominator that belongs to the Gaussian surface area. Then you can cancel the 4π's that are common to the numerator and denominator.

 

[jlmccart03]

Close. You're missing the r² in the denominator that belongs to the Gaussian surface area. Then you can cancel the 4π's that are common to the numerator and denominator.

Ok so that would mean it becomes (r³-a³)/(3ε₀r²))ρ?

 

[gneill]

Yes, that looks good.

 

[jlmccart03]

Yes, that looks good.

Phew! Thanks for the help even though I got really lost, but I really appreciate you working through the roadblocks I was having! Thank you!

 

[gneill]

You're welcome