Mathematical model for interaction force between magnetic fields?

[Psinter]

I wanted to know if there is a mathematical model to know the force with which a source of a magnetic field attracts or repels another source of magnetic field.

For example, the mathematical model for the electrostatic force a charged particle exerts over another charged particle is: $F = k(\frac{Q_1Q_2}{r^2})$

where:
$k$ is a constant with value 8987551788$\frac{Nm^2}{C^2}$
$Q_1$ is the charge of particle 1 in Columbus
$Q_2$ is the charge of particle 2 in Columbus
$r$ is the distance in meters between the center of each particleSo, is there a digested equation like that one but for magnetic fields?

 

[tannerbk]

I wanted to know if there is a mathematical model to know the force with which a source of a magnetic field attracts or repels another source of magnetic field.

Not sure exactly what you mean, but there is an analgous force law for magnetism. For a charge Q, moving with velocity v and magnetic field B, the Lorentz force law is $\textbf{F}=Q(\textbf{v} {\times} \textbf{B})$. Thus in the presence of both electric and magnetic fields, the net force on some charge Q would be $\textbf{F}=Q(\textbf{E}+\textbf{v} {\times} \textbf{B})$.

 

[physwizard]

The analogue to an electric charge is a magnetic monopole. The fact is that the magnetic monopole does not exist (at least it hasn't been discovered so far). You will never be able to get an isolated 'North' pole or an isolated 'South' pole. Even if you break a magnet into two each half will form its own north and south poles. In other words the magnetic poles exist in pairs, an isolated magnetic pole does not exist. Nevertheless, it is still possible to approximately describe the force between two magnetic poles by a law of a similar form as Coulomb's law. It would be more accurate though to treat a magnet as a magnetic dipole; this is analogous to an electric dipole which consists of a positive and a negative charge separated by a small distance.

 

[Psinter]

Not sure exactly what you mean, but there is an analgous force law for magnetism. For a charge Q, moving with velocity v and magnetic field B, the Lorentz force law is $\textbf{F}=Q(\textbf{v} {\times} \textbf{B})$. Thus in the presence of both electric and magnetic fields, the net force on some charge Q would be $\textbf{F}=Q(\textbf{E}+\textbf{v} {\times} \textbf{B})$.

You replied and me just finishing of looking at that equation in the book. Hehe.

I'm still looking for something. What I mean is specifically for ferromagnetic materials like permanent magnets which do not posses moving electric charges.

I found this in Wikipedia: here and here

Can someone recommend some more literature on those subjects?

The analogue to an electric charge is a magnetic monopole. The fact is that the magnetic monopole does not exist (at least it hasn't been discovered so far). You will never be able to get an isolated 'North' pole or an isolated 'South' pole. Even if you break a magnet into two each half will form its own north and south poles. In other words the magnetic poles exist in pairs, an isolated magnetic pole does not exist. Nevertheless, it is still possible to approximately describe the force between two magnetic poles by a law of a similar form as Coulomb's law. It would be more accurate though to treat a magnet as a magnetic dipole; this is analogous to an electric dipole which consists of a positive and a negative charge separated by a small distance.

Yup just got that. Thanks.

 

[sardar]

Yes, there is a mathematical model for the interaction force between magnetic fields. It is known as the Lorentz force law and is given by the equation:

F = q(E + v x B)

where:
F is the force in Newtons
q is the charge of the particle in Coulombs
E is the electric field in Volts/meter
v is the velocity of the particle in meters/second
B is the magnetic field in Tesla

This equation shows that the force is dependent on the charge of the particle, the strength of the magnetic field, and the velocity of the particle. It also takes into account the direction of the magnetic field, as represented by the cross product of v and B.

If you are looking for a more simplified equation, you can use the equation for the magnetic field produced by a current-carrying wire:

B = \frac{\mu_0 I}{2\pi r}

where:
\mu_0 is the magnetic permeability of free space (4\pi x 10^-7 Tm/A)
I is the current in the wire in Amperes
r is the distance from the wire in meters

Using this equation, you can calculate the magnetic field produced by a source and use it in the Lorentz force law to determine the interaction force between two magnetic fields.