How Do You Calculate the E-field in an Electron Cloud Using Gauss's Theorem?

[SimranPaudel]

Homework Statement

Q) To a very rough approximation a heavy atom can be pictured to be a spherical with
charge ‘+Q’and radius ‘a’ embedded in a much larger sphere of negative charge (the
electrons). This negative sphere will have a radius ‘b’ (the atomic radius) and charge
distributed uniformly throughout its volume will be ‘–Q’. Find electric field intensity for
any radius larger than ‘a’.

Relevant Equations

E= (1/4pi E0)* (Q/R)

I tried to use the formula for electric field intensity but I feel like something is missing.

 

[BvU]

Hello @SimranPaudel ,

$\qquad$!​

I tried to use the formula for electric field intensity but I feel like something is missing.

Good intuition ! You are describing the contribution from the nucleus. You need to add the contribution from the electrons ...

Note that your relevant formula is incorrect (check the dimensionsn and use brackets).

$\$

 

[SimranPaudel]

Hello @SimranPaudel ,

$\qquad$!​

Good intuition ! You are describing the contribution from the nucleus. You need to add the contribution from the electrons ...

Note that your relevant formula is incorrect (check the dimensionsn and use brackets).

$\$

Thank you so much for your response. I have attached the one that I tried to solve. Can you please check if it is correct? Thank you <3

 

[BvU]

For $a<R<b\$ the expression you use for the contribution from the electron cloud is not correct. Are you familiar with the gauss theorem ?

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