It's almost a perfect storm of inconvenient equations. Magnetic field strength drops off as the cube of the distance, so you want to increase the current in the

It's almost a perfect storm of inconvenient equations. Magnetic field strength drops off as the cube of the distance, so you want to increase the current in the coil, but power loss (and thus heating) in the coil goes up as the square of the current, while field strength is only linear.