5: You have a solid spherical conductor of radius a with a net charge -Q which i

Question

5: You have a solid spherical conductor of radius a with a net charge -Q which is in equilib- rium. A student analyzes that situation and says the following: "I think that one-fourth of the charge is uniformly distributed at a radius of j and the other three-fourths is uniformly distributed at a radius of a. If all of the charge were at the surface then the energy would be high since all the charges would have very close neighbors. In my arrangement, the charges at the surface are now (on average) farther from their neighbors so their energy is lower. The charges inside the sphere do have a higher energy than they had before but what matters is that the total energy is now lower." Gauss' Law clearly implies that the student's reasoning is wrong since the student's charge distribution leads to an electric field inside the conductor. Explain why the student is wrong using an energy argument. Although you could calculate and compare the energy of the student's configuration and the correct one, I want you to explain this in words alone.

Explanation / Answer

the electrical energy is given by

E = F / q

where F is the force between the point charge and the original charge there exists an electric field inside the charge, the charge always tries to exist at the surface of the solid sphere so it is mostly an energy argumant

the students assumption is wrong since most of the charge resides at the surfave of the solid sphere and there will be no charge existing at the radius (a / 2)

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