How to increase the distance of effective reach of a magnetic field from an electromagnet
Although air can be magnetized, its relative permeability (\$\mu_r\$) is defined as 1 &mdash; about the same as copper and aluminum &mdash; which is about as weak as you can get.  So it does not conduct magnetic flux very well compared to iron (\$\mu_r=5000\$) or annealed iron (\$\mu_r=200k\$).

In order to have a high pull strength, the gap must be very small or the number of enamel insulated turns must be very large.

Fortunately, our bodies are not very magnetic except to very high >4 Tesla levels which can be used for imaging of excited electrons spinning out of orbit.  Where I once lived they developed a portable scanner for putting a patient inside the tube in an operating room that did not have metal in it.  They can distort the images of old CRT's under a 10 story building and accelerate a metal chair across a room up highway speeds towards the cryogenically cooled coils. But that's how MRI's work.

Unfortunately Op Amps do not conduct much current needed to make an electromagnet. But beware that when you open the circuit, the inductor stores the energy which must be released at the contacts creating a huge voltage. \$V=L\frac{di}{dt}\$ and \$dt\$ can get really small with an open wire.
For flux calculations: http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html#c3   

Now they are are trying to charge mobiles wirelessly and even EV's (electric vehicles) with 4kW at present, 12kW in labs and 18kW in future. In order to do this impedance matching sending and receiving coils need to be designed to minimize leakage and have a diameter at least 2x to 4x the gap.  

Less is more, as in flux coupling.