A region in space contains a total positive charge "Q" that is distributed spherically such that the volume charge density p(r) is given by
p(r) = 3ar/(2R) for r is less than or equal to R/2
p(r) = a[1-(r/R)^2 for R/2 is less than or equal to r which is less than or equal to R
p(r)=0 for r is greater than or equal to R
Here "a" is a positive constant having units of C/m^3.
Part A was: Determine a in terms of Q and R.
I got this part. The answer was 480Q/233* pi*R^2
Part B: Using Gauss's law, derive an expression for the magnitude of the electric field as a function of r for r is less than or equal to R/2. Express your answers in terms of the total charge Q .
And this part I tried. It must also have the variables R and r in it and it may have any other necessary constants.
The answer I got was 480Qr/(699*epsilon naut*pi*R^3) but that was wrong.
Part C:
Using Gauss's law, derive an expression for the magnitude of the electric field as a function of r for R/2 is less than or equal to r is less than or equal to R . Express your answers in terms of the total charge Q .
I didnt know where to start, but once again answer is in constants R, r, Q and any other necessary constants.
Part D:
Using Gauss's law, derive an expression for the magnitude of the electric field as a function of r for r is greater than or equal to R . Express your answers in terms of the total charge Q .
Once again I didnt know where to start, but once again answer is in constants R, r, Q and any other necessary constants.
Part E: What is the magnitude of the electric field E at r=R/2?
Please help, I really need it. And just as hopeful thing, but I'm very grateful for any hints or something to work with, I would like to know how to do the problem and understand it. Thanks :)
