The electric potential immediately outside a charged conducting sphere is 250 V, and 10.0 cm farther from the center the magnitude of the electric field is 440 V/m.
(c) Determine all possible values for the radius of the sphere. (Enter your answers from smallest to largest. If only one value exists, enter "NONE" in the second answer blank.)
V = keQ / R and E = keQ / R2
The Attempt at a Solution
Im assuming that since there are two answers (Im sure it is two definite answers), it has to do with the squared distance in the denominator of E; (+/-) a certain number. There is most definitely proportionality here.
My attempt hasnt gotten me far. I found the electric potential at the +10cm where the electric field is 440. That hasnt gotten me anywhere. I try to set up a system of two equations where 1) 250 = keQ/R1 ----> R = 210/keQ and 2) 440 = keQ/(R22+10) *radius should be given in cm*-----> (R22+10) = keQ/440
I have no idea where to go from here. My head hurts from this problem and I put so much time into it and got basically no where. Please help.