Magnetic ball falling inside conducting tube

AI Thread Summary
A magnetic ball with a specific magnetization is falling through a conducting tube, and the problem involves understanding the physics behind its motion. The ball is not rotating and is influenced by its magnetization, which is oriented downward. The individual is unsure how to approach the mathematical aspects of the problem, despite having a general understanding of the physics. They found a relevant paper that discusses similar concepts using monopole approximations but are uncertain about applying a dipole approximation for their spherical case. The discussion highlights the need for clarity on how to express magnetic flux in this context.
masterjoda
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Homework Statement


I have a magnetic ball with magnetization M, mass m and radius R that starts to fall from rest through conducting tube of radius a little big larger than R, thickness \Delta and conductivity \sigma. The ball is not rotating, it said that magnetization is oriented vertically down.

Homework Equations


Professor send me this problem, usually I know how to solve the problems that he sends me, but his one I don't know even how to start.
 
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They here use approximation with two monopoles but in my case I have a sphere and I think I sound me approximation with a one dipole but I don't know how to write flux then?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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