Scalar And Vector Potential Fields

For a solenoid, the vector potential is related to the magnetic field by the relation . For an ideal solenoid, the magnetic field inside is uniform and can be expressed as: where is the permeability of free space, is the number of turns, is the current, and is the length of the solenoid. Step 1: Magnetic vector potential in cylindrical coordinates The magnetic vector potential for a solenoid is given by the solution to Ampere's law. Inside the solenoid, the vector potential is azimuthal ( ) and depends on the radial distance : This equation indicates that increases linearly with inside the solenoid, and reaches a maximum at , the radius of the solenoid. Step 2: Behavior of the vector potential At the fixed point , the vector potential is strongest at the outer edge of the solenoid ( ) and weaker at the center ( ). Therefore, the correct graph that represents this variation is one where increases with and reaches a maximum at . This matches option (C). Thus, the correct answer is (C).