Consider a cylindrical \$N52\$ magnet with mass \$m_0\$ travelling in horizontal x-axis with initial velocity \$v_0\$ in \$-x\$ to \$+x\$ direction. It passes through an copper air core solenoid on its right side. The ends of the solenoid are connected to a measuring device that measures: current, voltage and the power as the magnet approaches, enters, travels through and exits the solenoid. Alternatively we can assume a small 80% efficient electric device connected to the solenoid. Let the cumulative power generated be denoted by \$P_1\$. Let the total number of turns in the solenoid be fixed to some chosen \$N\$.
Query: How do we calculate the parameters for the magnet and the coil such that for the given velocity \$v_0\$ maximum amount of kinetic energy is converted into power in the solenoid? And what is the maximum conversion efficiency we can achieve? Solenoid and device are fixed to the ground.
For the magnet: The length\$(l)\$ and diameter\$(d)\$ of the cylindrical magnet (their ratio \$(l/r)\$) (for a fixed mass \$m_0\$)
For the solenoid: The gauge or diameter \$d\$ of the wire, the 'shape' of the \$N\$ turn cylindrical solenoid. By shape we mean that all the \$N\$ turns can be in a single layer thus resulting in a long solenoid in one extreme case or a solenoid with \$t\$ turns in each layer and \$l\$ layers such that \$N=tl\$.
From Ohm's Law \$V = IR\$. The resistance is inversely proportion to the area of the cross section of wire, thus the larger diameter would lead to lesser resistance per unit length in a wire. Moreover the inner air core diameter should be as tight as possible w.r.t. the diameter\$(d)\$ of the magnet so that maximum number of field lines pass through the solenoid as the magnet passes through it.
But I don't know how to calculate these parameters. My background is not in EE so please take that into consideration.
