1. The cavity inside a neutral conducting spherical shell of inner radius a and outer radius b is filled with an insulating material that has a non-uniform charge density p(r) = Porla, where po is a positive constant. a. Find the electric potential as a function of r in every region of space taking V (r → ∞) = 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 working your way back to obtain the known electric field using ar c. A point charge q> 0 with mass m is moving from infinitely far away towards the center of the sphere in the radial direction. What is the speed of this point charge at r= 2b if it were to barely touch the outer surface of the shell before being reflected?
1. The cavity inside a neutral conducting spherical shell of inner radius a and outer radius b is filled with an insulating material that has a non-uniform charge density p(r) = Porla, where po is a positive constant. a. Find the electric potential as a function of r in every region of space taking V (r → ∞) = 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 working your way back to obtain the known electric field using ar c. A point charge q> 0 with mass m is moving from infinitely far away towards the center of the sphere in the radial direction. What is the speed of this point charge at r= 2b if it were to barely touch the outer surface of the shell before being reflected?
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Transcribed Image Text:1. The cavity inside a neutral conducting spherical shell of inner radius a and outer radius b is
filled with an insulating material that has a non-uniform charge density p(r) = Porla, where po
is a positive constant.
a. Find the electric potential as a function of r in every region of space taking V (r→∞) = 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 working your way back to obtain the known electric field
using
av
ar
c. A point charge q> 0 with mass m is moving from infinitely far away towards the center of
the sphere in the radial direction. What is the speed of this point charge at r= 2b if it were
to barely touch the outer surface of the shell before being reflected?
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Given:
The non-uniform charge density of the spherical shell is
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