Spherical symmetry doesn't permit the field configuration different from radial one. From the other side the circulation theorem implies tangent field with non zero rotor. The solution of Maxwell equation gives loss of symmetry and a hole in the sphere for ' charge supplying wire'. What's the matter?
There cannot be spherical symmetric current uncompensated by displacement current - that is charge conservation, it is also in the Maxwell's equation.
So the magnetic field will be 0.
I've put the clear example: the ball made of betha-decaying substance emitting in symmetrical manner high energy electrons ( E>0). Thus we receive spherical current density. The H=0 doesn't satisfy the circulation theorem if we choose as a contour any circle except of lieing in diametric plane. Voila!
'The H=0 doesn't satisfy the circulation theorem if we choose as a contour any circle except of lieing in diametric plane. Voila!'
True, but the sphere will be charged and build up electric field (displacement current). The displacement current will be responsible of cancelling the impact of current.
Thnx, Nikolay. I didn't think about this factor at all implying thin wire supplying charge to the ball. But this wire changes completely situation.
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