Determine the number of times the magnetic field has wound around the Sun

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To determine how many times the magnetic field has wound around the Sun at a heliocentric distance of 70 AU, one must relate the circumference of the Sun to the distance traveled. The relevant calculations involve understanding the interplanetary magnetic field and its source, which is tied to the Sun's rotation. The magnetic field lines extend outward from the Sun, and the radial speed of these lines is crucial for the calculation. The angular velocity of charged particles in a magnetic field can also be factored in, using the provided formula involving mass, charge, and magnetic field strength. Understanding these relationships will lead to the solution of the problem.
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Homework Statement



Hi,
I know that this probably is easy to calculate, but I have the ability to thing the opposite about problems, therefore I'm stuck with this one. The question is

Determine the number of times the magnetic field has wound around the Sun by a heliocentric distance of 70 AU.

Homework Equations



I guess that I have to find a relation between the circumference of the Sun (or a circle generally) and the length of something, in this case L=70 AU. But as I mentioned, I really don't know what to do.

Is it relevant to determine where the magnetic field source is located? If yes, then R=10Rs (Rs = radius of the Sun).

The Attempt at a Solution

 
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You'll want to do some investigation on the topic of the interplanetary magnetic field. Find out where its base is "locked" to the rotation of the Sun, and how the field lines are carried outwards (what entrains the field lines?). Hint: find the radial speed.
 
I assume that the angular velocity for a charged particle in a magnetic field is:
T=2*π*m/qB ; m should be the mass of an electron (?) , q=the charge , B = magnetic field strength, which I have. And where it is "locked", isn't it the 10*Rs that I mentioned?
Thanks btw!
 
Take a look here to begin with.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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