Including the current's own magnetic field turns the sliding-bar Faraday problem into a damped electromechanical oscillator that maps onto a series RLC circuit with equivalent capacitance M/(l^2B0^2).
Feynman, Robert B
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The moving bar problem: an electromechanical damped oscillator
Including the current's own magnetic field turns the sliding-bar Faraday problem into a damped electromechanical oscillator that maps onto a series RLC circuit with equivalent capacitance M/(l^2B0^2).