A infinite long cylinders symmetric current distribution with radius R and a total current I > 0. the distributions current density J is time independant, parallel with the cylinder axis and has the size : J = k * r^4 , r =< R where r gives the distance to the cylinder axis and k is a konstant med dimensions A/m^6.
a) determine the constant k.
b) determine for all r sizes and direction of the magnetic field, that the current distribution makes.