I am trying to design a very powerful electromagnet for experimental reasons. However, I am wondering at his absurd sounding conclusion I arrived at! The governing equation of the magnetic field generated by a solenoidal electromagnet is B = u0nI Provided that I keep these things constant 1. length of solenoid = 15 cm 2. diameter of solenoid = 2cm 3. Voltage to be applied = 24 Volts 4. Max power = 72 watts. (hence max current = 3A) then I can increase B, by simply increasing n. But to increase n, I need longer wire, hence more R (resistance); so less than 3A current may flow if I wound more wires to increase n. However, I can always reestablish 3A current by simply increasing the wire diameter. Thus it seems to me that I can attain B as high as I desire, by simply winding more wire and increasing the wire diameter, and my electromagnet will never consume more than 72 watts. My intuition tells me this must not be possible, but I don't see why?