Electric Field inside an insulating sphere

[zgs]

1.
I think this should an easy one:

Homework Statement
Consider an insulating sphere of radius R centered on the origin with total charge Q uniformly distributed throughout the volume of the sphere. What is the electric field E inside the sphere at a distance r from the origin? (i.e. r<R)

Homework Equations

They list Vshpere=4/3 ∏r^3 and Asphere=4∏r^2
I know E=kQ/r^2=f/q

The Attempt at a Solution

Multiple choice and I thought it was just E=kQ/r^2. Answer is really E=kQr/R3. Where did R^3 come from? I have to be missing an equation from my notes.. I must have to somehow incorporate the volume.

 

[Muphrid]

This requires a little thinking. The Q in the kQ/r^2 formula represents the charge of a point charge. That isn't the Q you're given. This is a fairly standard trick to fool students who memorize formulas without understanding the full meaning of the variables. To be fair, real physicists make the same mistakes sometimes, too.

Tell me: how much charge is enclosed by the chunk of sphere out to a radius r?

 

[zgs]

Tricksters. It would still be Q because it is uniform. Right?

Edit: *All of it?

 

[zgs]

I got it! Ignore the above reply. Vr / VR = r^3/R^3. Multiply that by original equation, and that gets the right answer. So to sum it up for my sake of remembering on the exam; the Q is the whole sphere (a point at a distance) and to get the enclosed chunk I find the ratio of it to Q. -not the most clear summation of thought but I get what I'm trying to say I think. Thank you for getting my brain turning.