Two sufficiently long, smooth conductive rails are placed parallel to each other in a horizontal plane, separated by a distance L. A capacitor with capacitance C and a resistor with resistance R are connected in series at the left end of each rail. A uniform magnetic field (magnetic flux density B) is applied vertically upward, perpendicular to the rail surface, in the space containing the rails.
Now, a conducting rod of mass m is placed perpendicular to the rails. Starting from a stationary position at time t=0, a constant external force of magnitude F is applied parallel to the rails and directed to the right, causing the conducting rod to be pulled. The resistance of the conducting rod and rails, the self-inductance of the circuit, and friction and air resistance are all negligible. The capacitor has no initial charge.
After a sufficient amount of time has elapsed since the conducting rod was started to be pulled, the magnitude of the current flowing through the circuit approaches a constant value I. Find the algebraic expression for this magnitude I.
The magnitude of the current I [A] after a sufficient amount of time has elapsed is expressed as an irreducible fraction qp (where pandq are relatively prime natural numbers). Enter the value of the sum of the numerator and denominator, p+q.