# Minqi 02 Apr 2016 - 2

## Question

The figure below shows the cross section of a long cylindrical magnet, as well as the plan view of the radial magnetic field. The cylindrical magnets are placed vertically. A thin circular aluminum ring of radius r and resistance R falls through the magnetic field as shown in the diagram. In the vicinity of the aluminum ring, themagnetic flux density is 2.0 T.

[Resistivity of aluminium = 3.1 x 10-8 Ω m, density of aluminium = 2.7 x 103 kg m-3]

a) By considering the plan view of the magnet, indicate the polarity of the magnets and the direction of the induced current.

b) Describe the motion of the aluminum ring when it is released in the radial magnetic field.

c) Show that the current in the aluminum ring when it is falling at a speed v is given by

$$I= {{2 \pi r B v} \over {R}}$$

d) Calculate the terminal velocity of the ring.