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So my take on this is, if R is larger than d, then the infinitely long line will strike through the sphere.

I set this up as electric flux(f) = EA = Charge in sphere(q)/permittivity of free space(e)

so f = EA = q/e

The area of the sphere is 4(pi)r^2

q = (halflife)(length)

So f = E4(pi)r^2 = (halflife)(length)/e

so E = (halflife)(length)/e4(pi)r^2

I know the correct answer is ((2halflife)/e)(square root of (R^2 - d^2)

If anyone can help me out it would be greatly appreciated, I think I am on the right track, but I just cannot figure out how to go from the answer I have to the answer in the back of the book. I appreciate anyones help who takes the time to read this!

Josh