A capacitor has been charged to , a metal bar with mass m ,resistor R is located between two parallel wire (distance L) in magnetic field B, as shown in the above figure.
At t=0; the switch was turn from a to b.
Current I will flow throught metal bar, which F=I L B will accelerate meta bar. .
When the metal bar is moving, the changing in magnetic flux will induce voltage
So the equation for the loop is , where
the solution is ,where
The following is a simulation for the above case:
The charge , the velocity and the current are shown (C=1 in the calculation).