Due to space constraint, I wanted to set up two coils over each other. (So one coil is wound on a spool, then I want to wind the other coil over it (not necessarily touching it.))
However as it will cause them to effect each other (as it behaves like a transformer), I was looking for a solution to isolate the two.
Do you guys have any suggestions to achieve the same?
You can't eat that cake then suddenly discover it's still there. The two coils couple magnetically so any ac signal on one will be transferred to the other albeit in a smaller amount depending on turns ratio, coupling factor and loading.
If you want to isolate them then move them apart or set up a high frequency field and run one coil like a metal detector - because it will be tuned it will largely ignore the impulse to drive the projectile and only modulate the RF field as the projectile moves. Far more complex but do-able if you know how.
This is impossible due to Ampere's law and Faraday's law.
Faraday's law:
The induced electromotive force in any closed circuit is equal to the negative of the time rate of change of the magnetic flux through the circuit.
http://en.wikipedia.org/wiki/Faraday%27s_law_of_induction#Faraday.27s_law
Ampere's Law states that for any closed loop path, the sum of the length elements times the magnetic field in the direction of the length element is equal to the permeability times the electric current enclosed in the loop.
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/amplaw.html
When you start running current through one of the coils, it will cause a changing magnetic flux as the rate of current flow increases (by Ampere's law). This changing magnetic flux will induce a current in the other coil (by Faraday's law). You might be able to guide the magnetic flux with a chunk of metal, like is done with a transformer, and possibly even isolate these coils almost completely, but, this means that no point in space would share flux lines between the two coils. This is implied by Ampere's law which doesn't specify the shape of the loop you integrate around. On the one hand, this gets rid of your mutual inductance problem but, on the other, it completely defeats the purpose of your device, which requires having a projectile interact with both coils. At best, it could interact with just one.
http://en.wikipedia.org/wiki/Inductance#Mutual_inductance_of_two_wire_loops
So how do you accomplish what you need? You have two options:
Since I don't know the arrangement possibilities of your project, I can't propose a working idea. But I can review the relevant theoretical background.
We can consider as a coaxial Helmoltz coils. In this case the mutual inductance depends not only on the coil length and diameter but also on their relative position, and never forget in calculations that the field direction it is a vector. If L1 and L2 are the self-inductances and Lm is the mutual inductance between coils, the total inductance will be Ltot=L1+L2±2Lm.
the mutual inductance is at maximum when they are also concentrical, i.e. D=0
If the two concentrical coils are rotated, so that their axes are not parallel any more, the mutual inductance decreases, and becomes almost zero at 90°. Continuing the rotation beyond 90° the mutual inductance increases again, but this time with the opposite sign. So, at 180° gives a variation of the total inductance of 4Lm.
If the two coaxial coils are moved along their axis instead, the mutual inductance decreaes and becomes zero at infinity
btw there is in an excellent paper which is dealing in depth with this subject. Feel free to send an email to me.
