Question

Two resistanceless rails rest 20 cm apart on a 3.5 ? ramp. They are joined at the bottom by a 0.80 ? resistor. At the top a copper bar of mass 0.080 kg (ignore its resistance) is laid across the rails. The whole apparatus is immersed in a vertical 0.60 T field. What is the terminal (steady) velocity of the bar as it slides frictionlessly down the rails?

Answer 1

We will start by finding the force exerted by gravity on the bar. We know that the magnetic force will only pointto the right, as it needs to be perpendicular to the magnetic field and the current will run along the copper bar.Thus, the velocity will be terminal when there is no net force in thex-direction. We start with gravity

To find the magnetic force, we first find the change in flux per unit time, and, as a result, the emf around theloop:

We then use the Lorentz force law to find the force

And we set the gravitational force equal to the magnetic force

And we know thatvx=vcos?, so we find the final velocity