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I'm stuck on this question.

Q) A simple classical model of an atom consists of a nucleus a postive charge [itex] N\,e [/itex] surrounded by a spherical electron cloud of hte same total negative charge. ([itex] N [/itex] is the atomic number and [itex] e [/itex] is the magnitude of the electric charge) An external electric field [itex] E_0 [/itex] will cause the nucleus to be displaced a distance [itex] r_0 [/itex] from the center of the electron cloud, thus polarizing the atom. Assuming a uniform charge distribution within the electron cloud of radius [itex] b [/itex], find [/itex] r_0 [/itex].

A) Well I have the solution... but I don't understand it.

This is what the book does.

First find the electric field of the electron cloud.

[tex] \epsilon_0 = \oint_S \vec E_{el} \cdot d\vec s = 4 \pi R^2 \epsilon_0 E_R(R) = Q_{enc} [/tex]

Thus,

[tex] \vec E_{el} = \hat R \frac{Q_{enc}}{4 \pi \epsilon_0 R^2} [/tex]

So this vector function gives the electric field of the electron cloud as a function of distance from the orgin, correct?

Now the book moves onto saying that there are two distinct regions to consider:

(1) [tex] 0 \leq R \leq b [/tex]

(2) [tex] r \geq b [/tex]

It says,

However since [tex] r_0 > b [/tex] implies ionization of the atom, we will only determine [tex] E_{el} [/tex] for [itex] R < b [/itex].

I don't understand this. If we chose a point [itex] P > b [/itex] how does this imply ionization of the atom.

Wouldn't chosing a point just mean,

[tex] \vec E_{el} = \hat R \frac{Q_{enc}}{4 \pi \epsilon^2 (R_P)^2} [/tex]

where [itex] R_P [/itex] is the distance from the orgin to P.

doesn't this say, what is the electric field at this point. How does this have anything to do with removing the proton?

Would someone explain this?

Also,

The book calculates [itex] Q_{enc} [/itex] as follows:

The charge density of the electron cloud is given by:

[tex] \rho = \frac{-N\,e}{4/3 \, \pi b^3} [/tex]

For [itex] 0 \leq R \leq b [/itex] we have:

[tex] Q_{enc} = \rho \frac{4}{3} \pi R^3 = -N\,e \frac{R^3}{b^3} [/tex]

Why doesn't the [itex] Q_{enc} [/itex] enclose the nucleus?

I really just need some hand holding on this, because I'm lost and I have spent way to much time trying to figure this out. Thanks in advance!

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# Spherical Electric Field - displacing a nucleuo

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