Archive for June 11th, 2010

Physics Friday 123

June 11, 2010

Part 3: Vector Potential of a Solenoid

Consider the ideal, infinitely long solenoid of radius R, n turns per unit length, and carrying a current I. Let us use cylindrical coordinates (ρ, φ, z), with our z-axis on the axis of the solenoid, so that the field inside the solenoid is in the positive z direction (the current is in the positive φ direction). Then consideration of the symmetries and the right-hand rule indicates that the magnetic field is purely in the z direction. Consideration of Ampère’s Law in the integral form, , as described here over rectangular loops in a ρz plane indicates that the field is a uniform inside the solenoid, and vanishes outside the solenoid (see here). Now, what then is the magnetic vector potential (in the Coulomb gauge)?