Please answer the question in its entirety, and show your work! I will rate qual

Question

Please answer the question in its entirety, and show your work! I will rate quality answers! Thank you.

The system shown in Figure below is in the homogeneous magnetic field B = 0.1 T. The distance between two conducting vertical rails is l = 10 cm. A rod having a mass M = 10 g start moving in a gravitational field (initial velocity is zero), and it is always in electrical contact with the rails. The inductor has L = 1 mH. What is the magetude of acceleration of the rod as a function of displacement from initial position?

Explanation / Answer

at distance x from the initial position, while coming downwards
emf generated = V = Blv = Bl(dx/dt)
now, Bldx/dt = Ldi/dt
Bldx = Ldi
integrating
Blx = Li

and, magnetic force on the rod in magnetic field, F = Bil
so, from force balance we get
mg - Bil = ma

mg - B(Blx/L)l = ma
a = g - B^2*l^2x/L

this is acceleration og the reod as a function of displacement from the intial position

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