Gauss's law -- Integral form problem

jerryfelix30
Homework Statement:
The effective charge density of the electron cloud in a hydrogen atom in its quantum mechanical ground state turns out to be given by pnot(e^-(r/rnot)), where pnot is a negative constant (the clouds charge density at r=0) and rnot is a constant (rnot=0.025nm). Use gauss's law in integral form to calculate directly how E varies with r inside the electron cloud. Remember that there is a proton at r=0! Express your result in terms of the protons charge q.
Relevant Equations:
Gauss's law= E dot dA=q(enclosed)/epsilon not
Q enclosed is the net charge enclosed in the shape and epsilonnot is the permittivity constant
Problem Statement: The effective charge density of the electron cloud in a hydrogen atom in its quantum mechanical ground state turns out to be given by pnot(e^-(r/rnot)), where pnot is a negative constant (the clouds charge density at r=0) and rnot is a constant (rnot=0.025nm). Use gauss's law in integral form to calculate directly how E varies with r inside the electron cloud. Remember that there is a proton at r=0! Express your result in terms of the protons charge q.
Relevant Equations: Gauss's law= E dot dA=q(enclosed)/epsilon not
Q enclosed is the net charge enclosed in the shape and epsilonnot is the permittivity constant

The shape is a sphere so area is 4pi r^2
Ex4pir^2=q/epsilonnot
E=q/4pir^2(epsilonnot)

Homework Helper
Gold Member
You need to rethink what ##q_{enclosed}## is if your Gaussian surface is inside the charge distribution. If you have a shell of radius ##r## inside the cloud, what fraction of the electron charge ##e## is enclosed by this shell? Hint: An integral is required.

jerryfelix30
You need to rethink what ##q_{enclosed}## is if your Gaussian surface is inside the charge distribution. If you have a shell of radius ##r## inside the cloud, what fraction of the electron charge ##e## is enclosed by this shell? Hint: An integral is required.
So you have to take the integral from 0 to r for the charge density with dq?