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But how can this formula be derived and what principles are used for that?

I am thinking about assuming that magnetic flux is conserved, ##4\pi R_\odot^2 B_\odot=4 \pi r^2 B(r)##. Thus ##B(r)=B_\odot \Big(\frac{R_\odot}{r}\Big)^2##, but the exponent is 2 instead of 1/2.

Why am I wrong? Doesn't the magnetic flux conserve?