Let's say for the: First 10 milliseconds: Current is 1 milliamp. The squared magnetic field resulting we will call "default". 1 millisecond following, last millisecond: Current is -10 milliamps. The squared magnetic field is -100 * "default". The time average square of the magnetic field corresponds to: 10 * 1 - 1 * 100 = -90 One could then imagine the ability for an electromagnetic field made this way to do net work with zero net charge flow, provided that the time constant of the wire is larger than 10 milliseconds. Capacitors could easily increase the time constant of the circuit. The capacitors could be lined up in circuit with a low voltage battery. The circuit could intermittently connect and disconnect a higher voltage, higher current battery with the opposite polarity for a fraction of the time. If timed precisely, the charges would travel back in forth through the wire in a linear way while producing time-average squared magnetic field that is positive. Something is wrong.