Determine the force with which the magnetic field of a coil acts on an infinitesimal cube of iron

[withoutname]

Homework Statement

Determine the force with which the magnetic field of a coil acts on an infinitesimal cube of iron

Relevant Equations

F = q_0 v B don't work

Hi there,

I am working on a research paper and I need to determine the force with which the magnetic field of a coil acts on an small (pink-pong sized) iron ball. I tried to search for the force, acting of three dimensional object in magnetic field, but the only force I found was: F = q₀vB
I read other similar posts in Physics Forums ( this, this and this) and PhysicsStackExchange, but I understand only that the force depends on how far is the object from the coil. I think, that if I know the force with which the magnetic field of a coil acts on an infinitesimal cube of iron, I can make some integrations and find the answer. So can someone say what is this force? I will be very thankful if You include sources from where I will be able to read about this force!

Thanks a lot!

 

[berkeman]

If the magnetic field is uniform, is there any net force on the cube? Is the magnetic field from a finite coil uniform?

 

[withoutname]

If the magnetic field is uniform, is there any net force on the cube? Is the magnetic field from a finite coil uniform?

I think that the magnetic field of finite coil isn't uniform. At all I am using a coil with small lenght (not like a solenoid). So the magnetic field won't be uniform. As I know the magnetic field inside infinitely long solenoid is uniform, but our case is not such.

 

[nasu]

The force on a small dipole (as you may model your piece of iron) will depend on both the magnitude of the field and the gradient of the field at the location of the dipole. So, the first thing you need is the actual map of the magnetic field of the coil. Not just a single value of B but B as a fucntion of position, at least in the neighbourhood of the coil. Until you have this there is no point to look for the "right formula".

 

[withoutname]

Hi!
Thanks for the answer!
Do you think that this force can be found using Biot-Savart's law? I mean, to use

and then integrate over the whole coil.

 

[nasu]

Do you mean theoretically or practically?
I mean, in principle you can find the field of any configuration of currents by using Biot-Savart law. You will need a mathematical model of this distribution. It could be an analytical or a numerical model.

 

[withoutname]

Do you mean theoretically or practically?
I mean, in principle you can find the field of any configuration of currents by using Biot-Savart law. You will need a mathematical model of this distribution. It could be an analytical or a numerical model.

Theoritically. I am using Biot - Savart's law to find the magnetic field in some point. But can someone say, how then I can find the force acting on my particle?