= Solution
For motion to the right in $B_0\mathbf e_z$, $B_0>0$, the induced current is clockwise. Its own <magnetic field> points into the page inside the circuit, opposing the increase in external flux, as required by <Lenz's law>. As that current changes, its changing flux also produces an electromotive force opposing the change in current: the circuit has <inductance>.
Consequently the algebraic current law used in parts (i)-(iv) must be replaced by a dynamical circuit equation that includes the derivative of the self-flux. The induced current cannot in general adjust instantaneously to the bar velocity. Energy is temporarily stored in the self-field and can later return to the motion or be dissipated; the simple exponential braking law can change. Self-field forces and changes of inductance with circuit geometry may also matter. \b[The magnetic self-field changes the transient dynamics but does not create energy]: mechanical energy, magnetic-field energy and Joule heat must be included in the conservation balance. A quantitative answer would require the circuit's inductance and its dependence on $s$.
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