- #1
Silversonic
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- 1
Homework Statement
Using Ampere's law, show that the magnetic field strength in a region within a cylinder, which has a constant current density j (flowing in the direction parallel to its axis), is equal to
B = (mu-nought)*j*r/2
The Attempt at a Solution
It doesn't say specifically, but this is the field in the theta-hat direction - i.e. in the direction of the cylinder's axis of rotation. I can prove this easily and the actual question isn't the problem. I'm assuming that this question means I have to show that the magnetic field in the r-hat direction (radially outwards) and the z-hat direction (in the direction of the current flow) are both zero.
I can prove there is no component in the r-hat direction by taking an imaginary cylinder, placing it within and using the fact that the flux through the cylinders surface is always equal to zero.
However, how do I prove that there is no component in the z-hat direction? Any help/hints appreciated.