Electric field (easy at least I thought so)

[Kalie]

The electric field strength 5.0 cm from a very long charged wire is 2000 N/C.
What is the electric field strength 10.0 cm from the wire?

Okay I thought that since the radius is double what it was before using the equation:

E= K*q*(r head)/(r^2)

I said that it decreases 1/4 and becomes 500.

Thats wrong. But obviously because I ignored r head...the vector thingy. But how do I apply it to the equation and solve for its new value?

Sigh...confused

 

[mjsd]

think about the symmetry... for a point charge the field is distributed in all direction (a spherical gaussian surface), for a line of charges (the lateral surface of a cylinder)... so in other words, you have used the wrong formula. Use Gauss's law to derive a new a formula (E as a fn of r)