The direction of the magnetic field between the two cylinders while the capacitor is charging is counterclockwise.
According to Maxwell's law of induction, a changing electric field induces a magnetic field, B given by the equation
∫B.ds = μεdΦ/dt where ds = path length of magnetic field, μ = permeability of free space, ε = permittivity of free space and dΦ/dt = rate of change in electric flux. The electric field in the cylindrical capacitor is directed from the inner cylinder to the outer cylinder since the inner cylinder is positive and outer cylinder negative.
For an electric current which increases, the rate of change of electric flux is positive and this produces a magnetic field in the clockwise direction.
Since in this case, we have an exponentially decreasing current, dΦ/dt is negative. Thus, this will produce a magnetic field opposite to that of an increasing current. So, the direction of the magnetic field would be counter clockwise.
So, the direction of the magnetic field between the two cylinders while the capacitor is charging is counterclockwise.
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