# Gauss' law-thin spherical shell

Gauss' law---thin spherical shell

INTRODUCTION- hello, actually i had been doing some problems on gauss' law from H.C.Verma "concepts of physics". i'm continuously having problem with "wht's the field on the surface of a thin spherical, conducting shell?

THE EXACT PROBLEM IS- "Consider the following very rough model of beryllium atom. the nucleus has 4 protons and 4 nutrons confined to a small volume of radius 1E-15 m. the two 1s electrons make a spherical charge cloud at an average distance of 1.3E-11 m from nucleus, whereas the 2 2s electrons make another spherical cloud at an average distance of 5.2E-11 m from the nucleus. Find the electric field at (a)a point just inside the 1s cloud and (b)a point just inside the 2s cloud. please help."

THE WAY I TRIED TO SOLVE- for a point just inside the 1s cloud the electric field wud be due to the nucleus, thats for sure. but wht abt the charge on the 1s cloud? wont that produce an electric field at the point? if not, then why? this is where i'm facing the problem.

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Sounds like you have two spherical shells

can anyone please help me by saying how to solve this problem?   i've just learned this gauss' law concept, so its really difficult for me to apply it at the right places. please help me and please dont mind. thanks...

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I apologize I haven't learned latex yet, so this formatting might be a little hard to read.

Basically Gauss's law is helpful because it tells you the amount of charge at a given point (the flux). Gauss' law states that the integral of E dot dA is equal to the amount of charge enclosed divided by epsilon-nought. To apply Gauss' law you need to do the following steps

1. Verify that there is symmetry. This symmetry will help you to decide which Gaussian surface you will be using (Gaussian sphere, Gaussian cylinder, or Gaussian cube). When selecting the Gaussian surface, make sure that the electric field is constant everywhere. I believe you can still use Gauss' law without symmetry, but it is not very useful and often incredibly complex.

2. Draw a picture of the field you are trying to find. Use a Gaussian surface to enclose the charge. I'll let you decide which Gaussian surface to use. The radius of the Gaussian surface should be equal to the distance from the point charge to the point in space where you are calculating the field.

3. Now, that you have enclosed the charge in a Gaussian surface you can start to apply Gauss' law. Start with the part about flux being equal to the integral of E dot dA. Knowing that E is constant, what can be done to make evaluating the integral easier? Also, remember this is a dot product. (a dot b = ab cos (theta)). What is the angle between E and dA. Keep in mind that dA is directed outward normal to the Gaussian surface.

4. Now, that you have calculated that integral, you will need to work on the other part of the equation. This says that the previous integral is equal to the total charge enclosed by the Gaussian surface divided by epsilon-nought. How would you calculate the total charge enclosed? Keep in mind the concept of superposition.

5. Now, you have both sides of the equation. Simply resolve / manipulate the integral until you have an equation in the form of E =...

If anything is unclear, please ask. I just learned Gauss' law myself last week so it might be helpful if a more advanced physicist could look over the steps I've written out 