- #1
individual61
- 3
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Hi all,
The situation is this: I need to calculate the self inductance of two solenoids wired in series, of equal radius and a given separation d. They are coaxial. The length h of each is known.
Most double-solenoid references I found looked at the mutual inductance, and not the self-inductance of this setup. This is not a transformer, but rather a magnetic quadrupole trap for cold atoms. The coils must be wired in series (and not from separate sources) so as to have identical currents. The ultimate goal is to be able to calculate the turn-on time of the trap for different winding numbers.
Just as background, the coils will probably be made from hollow copper tube (1/8 in OD ACR tubing), will probably not contain more than one layer of winding, the radius will be about 1.5 cm, and the separation, about 3 cm.
Attempt at a solution: Nothing too concrete yet. This isn't as simple as treating the system as an RL circuit with series inductors, because the magnetic field of one coil is very much a part of the flux of the other.
I was considering some very crude boundary values for the total self inductance using the simple solenoid formula:
[tex] L = \mu_0 n^2 l A [/tex]
where n is the number of turns per unit length, l the length of the solenoid, A its cross-sectional area.
I can calculate the value for a full solenoid using l = h + d + h and the physical winding density, then perhaps using the average winding density (N + N turns along h + d + h length).
Anyway, ideas and suggestions are welcome. As I mentioned, I am just aiming for a back-of-the-envelope calculation to see of the coils will have the right response time.
Cheers,
Paul
The situation is this: I need to calculate the self inductance of two solenoids wired in series, of equal radius and a given separation d. They are coaxial. The length h of each is known.
Most double-solenoid references I found looked at the mutual inductance, and not the self-inductance of this setup. This is not a transformer, but rather a magnetic quadrupole trap for cold atoms. The coils must be wired in series (and not from separate sources) so as to have identical currents. The ultimate goal is to be able to calculate the turn-on time of the trap for different winding numbers.
Just as background, the coils will probably be made from hollow copper tube (1/8 in OD ACR tubing), will probably not contain more than one layer of winding, the radius will be about 1.5 cm, and the separation, about 3 cm.
Attempt at a solution: Nothing too concrete yet. This isn't as simple as treating the system as an RL circuit with series inductors, because the magnetic field of one coil is very much a part of the flux of the other.
I was considering some very crude boundary values for the total self inductance using the simple solenoid formula:
[tex] L = \mu_0 n^2 l A [/tex]
where n is the number of turns per unit length, l the length of the solenoid, A its cross-sectional area.
I can calculate the value for a full solenoid using l = h + d + h and the physical winding density, then perhaps using the average winding density (N + N turns along h + d + h length).
Anyway, ideas and suggestions are welcome. As I mentioned, I am just aiming for a back-of-the-envelope calculation to see of the coils will have the right response time.
Cheers,
Paul