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Calculate the magnetic field inside and outside an infinitely long solenoid of radius R that carries...

Calculate the magnetic field inside and outside an infinitely long solenoid of radius R that carries a current I and has N windings per meter (pretend that the windings are circular). Make sure that you use symmetry to show that some components of the magnetic field are zero, and indicate the symmetry operations you use to do so. Also makes sure that you make drawings of the 3 Amperian loops that you use and indicate which part of the integrals are zero and why.

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