Two identical bar magnets are dropped simultaneously from rest through two identical, very long vertical copper tubes, Tube A and Tube B. Tube A is maintained at room temperature, while Tube B is cooled to a much lower temperature using liquid nitrogen. If v_A and v_B are the respective terminal velocities reached by the magnets in Tube A and Tube B, which of the following relationships is correct?

Step-by-step solution

When a magnet falls through a copper tube, it induces eddy currents that create an upward magnetic drag force. The terminal velocity is reached when this upward drag force exactly balances the downward gravitational force ( mg ). The induced EMF is proportional to the velocity v of the magnet. The induced eddy current I is given by I = EMF R , where R is the electrical resistance of the copper tube. Thus, the upward drag force F_ drag I v R . At terminal velocity, F_ drag = mg . Therefore, v R must be a constant fo