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By Ampere's law, in a cylinder, with a uniform (uniform across the circular cross section) current density directed along the axis of the cylinder, you will immediatey get a phi component of B that is proportional to r, just like you wanted. So try applying a volume uniform current density throughout the cylinder and in the axial direction.

Hi Robert,

Thank you for your response. I actually did this a bit ago, but unfortunately, due to other reasons that are not worth going into here, this method will not work well for what I would like to eventually do. It is possible, but I'd like to try doing it a differemt way. Is this method my best bet, or is it possible to just specifiy the field value on the boundaries and generate the field this way?

Thank you, Henry

Perhaps you could explain further what you are really trying to do? In a static model, the presence of the (curl of the) magnetic field and the presence of a current density are not independently specifiable. Curl B = mu0 J. And your field (as you require it) has a non-zero curl, so you need to have a non-zero current density.

Hi Robert,

I'm trying to model an exotic form of matter that for all intensive purposes adds a source term to Maxwell's Equations that behaves like a current density, but is not an actual current density. Essentially in the region where the matter is, Maxwell's equations are slightly modified, but again there is technically to actual current density. I'd like to eventually put in a detector model to simulate the response of the detector, but right now I'm just trying to impose a background field.

Thanks, Henry

Well, based on that, I admit I don't know the best approach here. My first thought would be to simply include the current density needed to generate the field anyway. Then you could (perhaps) not have to modify Maxwell's equations. After all, we are talking about a simple, uniform, static vector field of current density. If you don't like seeing that field later in your computations (which I presume may contain other currents), then you can always subtract it from your results for those currents. Your only problem handling it this way is if the presence of this background current somehow interferes with the other physics happening in your problem. Good luck. Maybe someone else has a better suggestion.