Question: 4. (20pts.) The cavity inside a neutral conducting spherical shell of inner radius a and outer radius b is filled with an insulating material that

4. (20pts.) The cavity inside a neutral conducting spherical shell of

4. (20pts.) The cavity inside a neutral conducting spherical shell of inner radius a and outer radius b is filled with an insulating material that has uniform charge density p > 0. (a) Find the electric potential as a function of r in every region of space taking V(r -> co) = 0. Hint: Find the electric field first using Gauss' Law and start finding the potential in the region r > b to work your way inwards. (b) Test your results from (a) by finding the known electric field using Ov E = r . ar (c) A point charge q > 0 with mass m is moving towards the center of the sphere. What is the speed of this point charge at r = 2b if it were to barely touch the outer surface of the shell before turning back

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