Can I increase range of a near field magnetic inductor from 10cm to 100cm by increasing radius of ferrite rod coil by 30 times?

I am interested in increasing the range of NFMI - near field magnetic inductions, used in hearing aids.

However the limiting factor is a range of 10cm, typically seen in hearing aids with a coil diameter of 1.5mm.

According to the magnetic field strength formula

According to the formula: A desired magnetic field intensity(B), can be achieved at an increased distance(r) of 100cm, with a radius(a) increase of 31.7 times the initial radius

Am I right in assuming this, or will there be practical problems/ unseen effects for such an antenna with large radius to work with magnetic induction of low frequencies such as 10MHz.

• Is this for a standard loop hearing-aid system? Can you add a little more information in your original post to give some context. I have installed some loops for friend and he is very happy with the results. – Transistor Aug 2 '16 at 8:54
• It's common to use transmitter antennas with a radius of 50m or more. The problem with increasing the sensitivity of the receiver is that you increase the sensitivity to noise. – david Aug 2 '16 at 10:24

On the other hand if the radius increases by $\sqrt{1000}$ then you receive the same magnetic flux density. For confirmation of your formula see this: -