What Is the Electric Field and Potential of a Spherical Charge Distribution?

[FourierX]

Homework Statement

A spherical charge distribution is given by

\rho = \rho_0\left(1-(r^2/a^2)) , (r<= a)
\rho = 0, (r> a)

a) calculate the total charge Q
b) find the electric field intensity E and the potential V outside the charge distribution
c) find E and V inside
d) show that the maximum value of E is at (r/a) = 0.745
e) the above charge distribution applies roughly to light nuclei. Draw graphs showing \rho, E, and V as functions of r/a for calcium (atomic number 20), assuming that \rho_0= 5.0 x 10^25 C/m^2 and a = 4.5 femtometers<br /> <br /> <br /> <br /> <br /> <h2>Homework Equations</h2><br /> <br /> [\tex]\oint E.da = Q/\epsilon_0[\tex]<br /> <br /> <br /> <br /> <h2>The Attempt at a Solution</h2><br /> \ Guass&#039;a law and other general equations for E and V were used. I do not think I am close to the correct answer.

 

[borgwal]

(a) follows from the definition of charge *density*; there is no need to use Gauss's law

(b) and (c) do follow from Gauss' law: choose the right surface and volume, and find E as a function of r. From that, obtain V(r).

 

[FourierX]

Thanks borwal, yeah that's what I've done. I am not quite sure about d and e, those are my real problems. Listed all the questions just let the entire problem be clearer. thanks for replying :)

 

[borgwal]

If you have E as a function of r, it should be rather easy to find its maximum!