Magnetic field due to a solenoid.

[PhysicoRaj]

Hi.
I have a solenoid, of length l, radius r, which has n turns of copper wire wound on it, carries a current of I amperes, and has a ferromagnetic core of relative permeability μ_r. How do I determine the magnetic field at a point in free space, x meters from the center of the solenoid?
Also, how to calculate the force of attraction experienced by a ferromagnetic substance(whose magnetic properties are known) due to the same solenoid, placed at that point?
Thanks for any reply.

 

[Simon Bridge]

Add up the fields due to each turn individually.
For most purposes you'll use an approximation, and design the solenoid so the approximation is good.
For complete nit-picky detail in the classical regime, you will have to add up the contributions due to each small section of wire.

Have you tried looking these things up?
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html
http://en.wikipedia.org/wiki/Magnet#Calculating_the_magnetic_force

 

[PhysicoRaj]

Thanks.
The problem I came upon was that the field inside the solenoid will be influenced by the permeability of the core whereas the point I wish to measure the field is in a medium of different permeability.
I used B=μnI/l which gives the field inside the solenoid. For the field outside it, what expression should I use so as to switch over to the permeability of free space?

Can I use the below equation(total field by integrating the equation for a current loop) by just replacing μ_° by μ_°μ_r?
B=(μ_°/4∏)[nIr²/2(r²+x²)^3/2]
Wouldn't this mean the point is also in the same medium as the core?

 

[Simon Bridge]

That's pretty much it yeah - remembering how the feld changes at the boundary ... you basically have materials with different refractive indexes.

 

[PhysicoRaj]

Thanks a lot!