Example: Metal Cart

Problem

A DC generator is built using a metal cart with metallic wheels that travel around a set of perfectly conducting rails in a large circle. The rails are L m apart and there is a uniform magnetic ${\vec {B}}$ field normal to the plane as shown in Figure 1. The cart has a mass m and is driven by a rocket engine having a constant thrust F. A resistor R is connected as a load. Find The current as a function of time. What is the current after the generator attains the steady-state condition?

Figure 1 will be shown here