Understanding Ampere's Law in Cylindrical Shell Configurations

[cragar]

If i have two cylindrical shells one inside the other , Like a pop can inside a larger pop can.
And let's say they are infinitely long . And on the inner one i have a surface current and on the outer one i also have a surface current but in the opposite direction. The B field in between the 2 cans just depends on the current from the inner can. Is the reason that the current does not matter from the outer can because the field cancels itself , Can we use the same argument from a Gauss surface , Like the E field inside a spherical shell with charge Q.
The E field is zero . Sorry If my writing seems choppy.

 

[Born2bwire]

Due to symmetry, the observed magnetic fields in this problem can only come about by an enclosed current. So there has to be cancellation on the interior of your shells. Think about it this way, to avoid confusion we will consider on cylindrical shell of current and instead of a shell of currents you have vertical strips of currents of infinitesimal width. If we observe at the center of the shell, then let's take two strips on opposite sides of the shell (one on the +x axis and the other on the -x axis).

So the field at the center due to the one on the +x axis will be directed in the -y direction (assuming that the current is flowing in the +z direction). The field due to the current element on the -x axis is directed in the +y direction. Since the currents are the same amplitude (due to symmetry) then we see that they cancel out exactly. Obviously the situation at the center is the easiest to visualize but one should be able to solve for the internal field generally (by using the expression for the magnetic field of a wire and integrating it accordingly) and one should find that the general case is also zero.

 

[cragar]

ok thanks for your answer.