Acceleration of ball bearing near solenoid

[Jake110]

ok so I am making a few solenoids for a little project I am doing at home, I am making a mass driver. i thought it would look good on my uni application, and it would be fun to build.

anyway, I am using the equation http://img229.imageshack.us/img229/5841/equation1solenoidimg.png to find the magnetic flux density of the solenoid and I am using F=BIL to find the force the solenoid exerts on the ball bearing, then I am using a=f/m to get the acceleration. now i don't know if I am using the right equations or not because the acceleration i get is about 28000ms^-2 and that seems way to powerfull for what I am using. all my values are in meters, amps, Tm/A (for the permeability constant) and kilograms (wich are made into Newtons by dividing by g for the mass of the ball bearing)

ill just list what the values I am using are.
u0 = 1.26*10^-6
I = 425 amps
N = 60 turns of the coil
r1 = 0.0175 meters
r2 = 0.0195 meters
X = 0.16 meters
X2 = 0.22 meters
L = 0.06 meters
m = 1.529*10^-3 (its 0.015kg divided by 9.81)

i got the equation for the magnetic flux density from http://www.netdenizen.com/emagnettest/solenoids/?solenoid" and it said to use 1.26*10^-6 for the permeability constant if you using meters which i am.

i don't think i enter anything wrong in my calculations, i redid everything three times and still got a massive acceleration. so either i got something wrong or this thing is going to be crazy. ill attach the excel document i used for calculating the magnetic flux density, the acceleration is easy to work out from there.

 

[Bob S]

If you have 60 turns in 6 cm, your wire diameter is 1 mm. Is that correct? This is probably 18 Ga wire. Correct? Are you putting 425 amps in it? For how long? My ARRL handbook says 18Ga is good for about 2.3 amps DC.
Also, why are you dividing 0.015 Kg by 9.81 meters/sec²?
How are you calculating acceleration?

 

[Jake110]

the wire is 1mm thick with the plastic casing, i think its actualy 0.5mm thick. acceleration = force divided by mass(F=ma is Newtons second law of motion i think, rearange it for a=F/m). I am dividing 0.015kg by 9.81ms^-2 because 0.015kg is the weight and i need the mass and weight = mg (mass * gravity), unless that's wrong and i need to use 0.015 instead, it still gets 3000ms^-2 acceleration. i don't know what 18 Ga means, sorry. although I am thinking its not the right kind of wire since you said its only good to hold 2.3 amps DC.

im trying to find out how fast the ball bearing will move towards the solenoid so i can work out how long the magnet needs to be active.

 

[Bob S]

Shouldn't the force and acceleration depend in some way on the magnetic field in the solenoid? The way you describe the force, it doesn't depend on the magnetic field, so turn the solenoid off. You don't need the solenoid. Now, where does the force come from without the solenoid?

 

[Jake110]

im using the equation F=BIL to get the force (its Force = Magnetic Flux Density * Current * length of solenoid) so the force does depend on the magnetic field of the solenoid and since I am using the force to get the acceleration that also depends on the magnetic field. is the magnetic flux density not the strength of the magnetic field then?

 

[Bob S]

You might be using the force formula for the Lorentz force. The Lorentz force is given by
F = L (I x B)
The force is on a wire of length L carrying a current I in a magnetic field B. The product of I and B is a vector cross product, so the force F is perpendicular to BOTH I AND B. The formula does not apply to a ball bearing in a magnetic field.

 

[Jake110]

oh right. there's the problem then, I am using the wrong formula to get the force. ill try to look up the right one but if you know one i could use, feel free to tell me.