i have one electromagnet that works under 110v dc .
i am building a project that an arduino can detect when my electromagnet is powered on .
i have build this electronic schematic that works
Are any other methods (or any electronic part) that i could use to detect when i will get 110v dc in my input but without be necessary the polarity of the 110v dc as it is in my schematic .
Yes. A bridge rectifier may be the simplest way, but you could use an additional zener diode plus an optocoupler that accepts AC (by using two antiparallel photoemitters, for example). There are other ways as well.
By the way, these methods tell you when the 110 VDC is connected and on. You would need something else to tell you when current is flowing through the electromagnet.
How about a hall effect sensor to detect when the magnetic field is on or off. Cheap and very compact, interfaces directly with a digital or analog input and very low power.