Immediately outside a very long cylindrical wire of radius r1 = 1mm, the electric field is 40kV/m directed towards the wire's surface.
A hollow cylindrical metal tube with inner radius r2 = 3mm is now placed around the wire, to form a coaxial cable. What will be the charge per unit length on the inner surface of this tube? Explain
The main equation that I've been using is:
The Attempt at a Solution
-In a previous part of the solution, lambda (the charge per unit length) of the wire was found to equal -2.224 nC/m
-I think that this therefore means the charge on the inner surface of the cylindrical metal tube must therefore be positive?
-My intuition says that the charge per unit length on the inner surface of this tube should be the same as that on the wire but different signs. I think that because for any given portion of the coaxial cable, the length of the wire and metal tube will both be the same. The charge enclosed will also be the same for both the wire and metal tube because only the electric field strength diminishes with radius, not the charge enclosed.
-My intuitive answer would therefore be +2.224 nC/m but I'm far from definite on it.
Is my line of thinking correct or am I a bit off?
Thanks in advance.