Can someone help me find an equation for magnetic force?

[Gabrielle17]

The equation needs to describe the force between two magnets and should relate to distance, angular frequency, angular acceleration, and torque. I need to find this equation for a research project, but I just can't figure it out and I can't find it online. (I'm new to this website so if this is the wrong forum please let me know and I will post in the correct one.) Thanks!

 

[berkeman]

The equation needs to describe the force between two magnets and should relate to distance, angular frequency, angular acceleration, and torque. I need to find this equation for a research project, but I just can't figure it out and I can't find it online. (I'm new to this website so if this is the wrong forum please let me know and I will post in the correct one.) Thanks!

Welcome to the PF.

What kind of magnets? Electromagnets? Permanent magnets?

 

[Khashishi]

Also, what is the orientation of the magnets and the angles of rotation? The angular acceleration and torque shouldn't matter.

 

[David Lewis]

When you have a current-carrying wire in a magnetic field:
Force = (magnetic flux density) * current * (length of conductor)

 

[Gabrielle17]

Welcome to the PF.

What kind of magnets? Electromagnets? Permanent magnets?

It is relating to the spin and relaxation that occurs in human tissue because this equation should demonstrate a phenomenon of MRI, but I was told to treat the situation as if they are bar magnets

 

[Gabrielle17]

When you have a current-carrying wire in a magnetic field:
Force = (magnetic flux density) * current * (length of conductor)

I don't think there is any current in this situation, it is more like two bar magnets, thanks for the help though!

 

[Gabrielle17]

Also, what is the orientation of the magnets and the angles of rotation? The angular acceleration and torque shouldn't matter.

What happens is there are these bar magnets, essentially, that act on each other and cause the ones next to them to move, so the exact angle is changing. I'm not sure why they are necessary, but the person above me (with a PhD so she knows what she is talking about) told me the equation will relate to distance, torque, angular acceleration, and angular frequency.

 

[nasu]

Maybe there is some misunderstanding between you and this person above. The angular frequency looks very out of place in a formula for the force between two permanent magnets at rest. Unfortunately the force between two magnets depends on the actual shape and size of the magnets, besides the distance between them and their orientation. You can easily find the simplest case, two small magnetic dipoles and the formula for this case. For bar magnets you may find some semi-empiric formulas (based on some experimentally determined parameters). Do you even know the characteristics of your magnets?

 

[sophiecentaur]

It is relating to the spin and relaxation that occurs in human tissue because this equation should demonstrate a phenomenon of MRI, but I was told to treat the situation as if they are bar magnets

You need to give some context to this question and a reference to clear things up. So far, you could be referring to any of a number of things. Are you trying to understand how quantum theory relates to the way an MRI scanner works for tissues?

 

[jamesuad]

The force is perpendicular to both the velocity v of the charge q and the magnetic field B. 2. The magnitude of the force is F = qvB sinθ where θ is the angle < 180 degrees between the velocity and the magnetic field.

 

[nasu]

@jamesuad How would you use this to calculate the force between two magnets?

 

[Dyatlov]

Maybe this will help get you started.
A time-dependent magnetic field which has time-independent z component and a circularly polarized field representing a magnetic field rotating along the (x,y) plane is:
$B(t)=B_0\hat k+B_1(coswt \hat i - sin wt \hat j)$
The Hamiltonian for this field is:
$H=-c \vec B(t) \cdot \vec S$
The time evolution solutions for the TISE for this Hamiltonian yield a magnetic field:
$B=B_1\hat i+B_0(1-\frac \omega \omega_0)\hat k$
This is the large magnetic field used in the MRI machine.
The two bar magnets which you are talking about is the above mentioned magnetic field and the magnetic dipole moment of individual protons in the human body.
When a person is put in a MRI machine, the protons align with the big magnetic field.
When u send a RF wave in the field (this is due to a specific resonance), the spin of protons starts spiraling down and end up rotating on the plane perpendicular to the $B_0$ magnetic field part. This creates another rotating magnetic dipole moment which sends EM waves which are picked up by detectors in the machine. The intensity of this beam is proportional to the density of protons (concentration of water in the tissues). This allows differentiation of tissues. This intensity signal is plotted on a grey scale and you get cross-sectional images. After this, the spin relaxes and you get two relaxation times $T_2,T_1$ which vary from tissue to tissue.