A cylindrical capacitor (two circular metal plates in vacuum) creates an electric field profile. As a thought experiment, can I set up currents to make a magnetic field which completely matches this profile inside the cylinder?
The currents can be placed anywhere (e.g, outside the cylinder with 3D complexity), but I'd prefer to have divergent-free currents, so that all fields are static. To be clear, magnetic monopoles are not allowed (the reverse problem of coverting a solenoid's magnetic field is easily solved by placing electric monopoles on the cylindrical boundary).
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