PhysicsLAB AP Free Response Question
2003 C1 E&M

 
A spherical cloud of charge radius R contains a total charge +Q with a non-uniform volume charge density that varies according to the equation
 
 
where r is the distance from the center of the cloud. Express all algebraic answers in terms of Q, ρ, R, and fundamental constants.
 
(a) Determine the following as a function of r for r > R.
 
 i. The magnitude E of the electric field

 ii. The electric potential V

 (b) A proton is placed at point P shown above and released. Describe its motion for a long time after its release.

 
(c) An electron of charge magnitude e is now placed at point P, which is a distance r from the center of the sphere, and released. Determine the kinetic energy of the electron as a function of r as it strikes the cloud.

 (d) Derive an expression for ρo.

 (e) Determine the magnitude E of the electric field as a function of r for r < R.





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