(Solved): PROBLEM 3 of 6 ( 18 points) Answers without solution steps clearly shown will not be given any credi ...

PROBLEM 3 of 6 ( 18 points) Answers without solution steps clearly shown will not be given any credit. A uniformly charged nonconducting sphere of radius

is concentric with a charged conducting spherical shell of inner radius

and outer radius

. As shown in the figure, the electric fields at points

and

(at respective distances

and

from the center

) are equal in magnitude and opposite in direction. (a) (9 pts) Find electric field

at point

which is at a distance

from the center

. Express

in terms of

and unit vectors. (b) ( 9 pts) Suppose that a particle of mass

and charge

is projected from infinity toward the shell with an initial velocity directed radially inward. What initial kinetic energy

(in terms of

and

) must the particle have in order to reach the shell before reversing direction? Take

at infinity.