# Constant power delivered to coil, constant magnetic field?

1. Sep 2, 2008

### kmarinas86

In here, I am discussing DC, not AC. So things that only apply to AC won't apply here.

I realized based on the formulas I have found, only a change in actual power delivered to a coil can actually produce a change in the actual energy in the coil. In addition, I have found based on the formulas that the reactive power can only exist if the power is changing. Any constant power deliver to a coil is in effect wasted since there would be no way to do work with magnets that stay "on" all the time. It seems to me that a simply combination of DC electromagnet and regular "permanent" magnet use to make a simply motor relies on the change of current as a function of time

Since:
$I=sqrt(2E_{mag}/inductance)$

It follows that:
$\frac{dI}{dt}=\frac{d(sqrt(2E_{mag}/inductance))}{dt}$

In other words, doubling the rate that current increases with time may increase the energy in the magnetic field at a rate 4 times greater. While doubling voltage will cause the current to increase twice as fast in an electromagnet, it is not necessarily the case in high inductance electromagnets that the switch be on for long enough for the current to reach its maximum, where the power input is indeed four times higher (2x voltage, 2x current). The current seems to rise the fastest at the beginning, when the current is still low after the voltage is applied. Yet, the current rises most slowly when it is near the maximum as determined by the resistance, and although at that point the magnetic field has the most energy, the rate at which it changes is also the least.

If the other magnet was affected by this electromagnet and was somehow in sync with it, in what sense does the use of reactive power (changes in the magnetic field's energy over time) convert to real power so that energy in the system is conserved?