Electric field strength -- calculating distance from charge

[Iron_Man_123]

Homework Statement

At a distance D from a very long (essentially infinite) uniform line of charge, the electric field strength is 1000 N/C. At what distance from the line will the field strength to be 4000 N/C?

Homework Equations

E=kq/r²

The Attempt at a Solution

I know that E is inversely proportional like so: E~1/r²
hence by rearranging for 'r' I got: r~sqrt(1/E)
then I plugged in 4E because 4000 N/C is four times 1000 N/C: r~sqrt(q/4E)
and I got r~E/2 but the answer is E/4 and I don't know how?

Thanks in advance

 

[BvU]

HI,

You want to develop an expression for the electric field of a long line charge first. Your relevant equation doesn't fit that.

 

[Fab]

What is the relevant equation that fits this scenario then?