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Electric Field Inside a Hydrogen Atom 
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#1
Mar1208, 12:10 AM

P: 11

1. The problem statement, all variables and given/known data
A hydrogen atom is made up of a proton of charge + Q=1.60 \times 10^{  19}\; {\rm C} and an electron of charge  Q=  1.60 \times 10^{  19}\; {\rm C}. The proton may be regarded as a point charge at r=0, the center of the atom. The motion of the electron causes its charge to be "smeared out" into a spherical distribution around the proton, so that the electron is equivalent to a charge per unit volume of \rho (r)=  {\frac{Q}{ \pi a_{0} ^{3}}} e^{  2r/a_{0}} where a_0=5.29 \times 10^{  11} {\rm m} is called the Bohr radius Find the total amount of the hydrogen atom's charge that is enclosed within a sphere with radius r centered on the proton. 2. Relevant equations 3. The attempt at a solution do I just try and divide out the volume. 


#2
Mar1208, 12:45 AM

Sci Advisor
HW Helper
P: 1,275

Well one can presumably just integrate charge density from 0 to r to get charge enclosed.



#3
Mar1208, 01:00 AM

Sci Advisor
PF Gold
P: 1,542

Here's my guess:
between the proton and the electron, the electron's charge cancels out, since there is no charge inside a uniformly charged sphere. So if r is less than the electron's distance than charge = +Q. If r is greater than the electron's distance, outside a uniformly charged sphere, the sphere can be treated as a point mass at the center of the sphere. So outside the electron's position charge = +QQ = 0. 


#4
Mar1208, 01:12 AM

P: 11

Electric Field Inside a Hydrogen Atom



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