What is the Magnetic Flux of a White Dwarf Derived from the Sun?

[Aleolomorfo]

Homework Statement

The sun has a rotational period of 25 days. Finding the rotational period if it can shrink to form a white dwarf ($R_{WD}=10^3Km$). Knowing that the density of magnetic flux of the Sun on the surface is $1 Gauss$, finding the magnetic flux of the white dwarf.

Homework Equations

The Attempt at a Solution

For the first part I can use the conservation of momentum $I_{sun}\omega_{sun}=I_{WD}\omega_{WD}$ with $I\propto MR^2$ and also with the hypothesis that there is no loss of mass during the shrinking. I have found that the period is 4.4$s$. However, I do not know how to do the second part about the magnetic flux. Should not be the same? But I am not even sure about this conclusion which I see it has not a proof.

 

[jedishrfu]

How was flux computed for the sun? Is it related to the change in area from sun to white dwarf?

 

[Aleolomorfo]

How was flux computed for the sun? Is it related to the change in area from sun to white dwarf?

I do not know how the flux was computed for the sun, it is in the text of the exercise. If it is related to the change of area, I will make a proportion:
$$\frac{Flux_{sun}}{R_{sun}^2}=\frac{Flux_{WD}}{R_{WD}^2}$$

 

[tnich]

I do not know how the flux was computed for the sun, it is in the text of the exercise. If it is related to the change of area, I will make a proportion:
$$\frac{Flux_{sun}}{R_{sun}^2}=\frac{Flux_{WD}}{R_{WD}^2}$$

The sun is a rotating ball of plasma. What is the distribution of charge in the sun? How much magnetic flux will be generated as a result of its rotation? Will the distribution of charge in a white dwarf be similar? It's time to do some research and/or make some assumptions.
EDIT: I am leaving out entirely the dynamics of convection within stars, which I think will dominate the magnetic fields of both M-class stars and white dwarves.