Does an electromagnet lag its input?

What about a small resistor in series with the electromagnet? The voltage across the resistor will be in phase with the current, and thus the magnetic field. You need to be careful connecting the scope to 120 volt ac, of course. You could use a small transformer for isolation.

Chuck

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The magnets pull is more closely related to the current than the voltage, so if you can monitor the current (with a current transformer and burden resistor, perhaps) that would get you close to seeing a signal proportional to the force. The shift between current and force involves eddy currents circulating in the iron pole pieces. Those also contribute to the magnetic force, but they are not in phase with the coil current. You would need to add a linear Hall effect sensor to the electromagnet if you really want to see the field strength.

By the way, paralleling the coil with the right sized capacitor (the one that reduces the total current to a minimum) will bring the voltage almost in phase with the line current, but the coil current will still have the same phase shift with respect to that voltage. The line current will just be phase shifted with respect to the coil current by the addition of the capacitor current to the line.

It will lag, but by somewhat less than 90 degrees. It depends on the L and R values.

The pull on a nonmagnetized object is according to the absolute velue of the coil current, modified by various complicated magnetic effects.

A series cap can resonate out the inductance, and can potentially swing the coil current from lag to zero to lead, depending. It can also increase the current, maybe by a lot.

John