falling conductor in a magnetic field
hi,
i have a perfect conductor bar, sliding over two percect rail conductors under the influence of gravity.
the bar mass is m, and is length is L.
the bar falls in an uniform magnetic field B which is perpendicular to the bar and the rails (outside of the page), the circuit is closed from above by a resistor R and an inductor L2.
find the velocity of the bar, if it rests at t=0.
i used the change in the magnetic flux to find the electromoving power of the ciruit, and therefore the change (the circuit has inductor) in current as a function of the speed.
i then used the magnetic force that the field apply on the current in the bar to get an equation for the cange in speed as function of the current.
i got:
dv/dt=L*B/(m*c) * I  g
dI/dt=L*B/(c*L2) * v + R/L2 * I
the problem, is that this solution get an exponential growth in velocity, where without the current the result should be a power of 2, and with the current the fall should slow down.
can you please help me?
