An electron experiences a force of magnitude F when it is 5 cm from a very long, charged wire with linear charge density, lambda. If the charge density is doubled, at what distance from the wire will a proton experience a force of the same magnitude F?

The  distance of the proton is  

Explanation:

Generally the force experience by the electron is mathematically represented as

 Where   is the charge density of the charge wire before it is doubled

Also the force experience by the proton is mathematically represented as

Given that the charge density is doubled i.e and that the the force are  equal then

Now given from the question that   the distance of the electron from the charged wire is  5 cm

 Then  

see earlier

your answer is c! hope this : )