12 Volt vs a 24 Volt Motor

Question

I have read that using a higher voltage motor would need less current to get the same power. I understand that P = IV and how that works. My question is if the 24 V motor would get half of the current, wouldn't it have half of the torque as well since they are directly proportional? In that case I don't understand how the 24 V would be advantageous at all.

Typically when people talk about motors a higher wattage motor is "better". I don't understand physically how more watts makes the motor "better". It just means it uses more energy per second which I guess would mean it is all converted into mechanical energy but not torque? I don't understand the relationship there.

Answer 1

The simplest answer is that the 24V motor would have twice as many turns of wire than the 12V motor (with thinner wire to fit the same armature). So even though the current is halved, the magnetic field is the same.

Below is from http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html

24V would have 1/2 of current I, but number of turns, n, is doubled, so B stays the same.