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3. A long permanent magnet in the shape of right circular cylinder of length L and radius a is used to lift a small solid sphere of radius b (b<<a, b<<L) with magnetic permeability u and mass density p. The permanent magnet has magnetization M, uniform throughout its volume and parallel to its axis. The sphere is initially resting on a flat horizontal non-magnetic surface. Calculate the maximum vertical distance d between the center of the sphere and the pole of the magnet at which the magnet can lift the sphere (writing down algebraic equation for d constitutes solution of the problem). Calculate the terminal velocity of the sphere as it hits the pole of the magnet that is distance d above the center of the sphere.
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Transcribed Image Text:3. A long permanent magnet in the shape of right circular cylinder of length L and radius a is used to lift a small solid sphere of radius b (b<<a, b<<L) with magnetic permeability u and mass density p. The permanent magnet has magnetization M, uniform throughout its volume and parallel to its axis. The sphere is initially resting on a flat horizontal non-magnetic surface. Calculate the maximum vertical distance d between the center of the sphere and the pole of the magnet at which the magnet can lift the sphere (writing down algebraic equation for d constitutes solution of the problem). Calculate the terminal velocity of the sphere as it hits the pole of the magnet that is distance d above the center of the sphere.
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Step 1

Given:

Radius is b (b<<a,b<<L).

To calculate the maximum vertical distance between sphere centre and magnet's pole and terminal velocity of sphere.

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