Oops, I can't draw an inductor at paint

In the figure given below, the box is an inductor having inductance \(L\). A uniform horizontal magnetic field of strength \(B\) perpendicular to the plane is present. The rails and the rod are perfectly conducting . The rod has a mass \(m\), and length \(l\). Initially, there is no current in the inductor and the rod is at rest. At this moment, it is let free.Let us denote the maximum current, the maximum speed, and the maximum displacement from this position be \(i_{m}, v_{m}\), and \(x_{m}\) respectively.
If \(i_{m}v_{m}x_{m}\) can be expressed as \(am^bg^cL^dB^el^f\), where \(a,b,c,d,e\) and \(f\) are dimensionless constants, then find \(abcdef\)

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