Force between poles of two magnets

AI Thread Summary
The Biot-Savart law describes the magnetic field generated by electric currents, while Lorentz's force formula calculates the force on a moving charge within that field. The discussion highlights a gap in textbooks regarding the forces between the poles of magnets, specifically the attraction between unlike poles and repulsion between like poles. It introduces the potential energy of a magnetic dipole in a magnetic field, defined as U = -m · B. Derivatives of this potential energy can be used to derive expressions for forces and torques acting on the magnetic dipole. Understanding these concepts is essential for a comprehensive grasp of magnetism.
Meow12
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Homework Statement
What is the magnitude of the force between two magnets if their poles are separated by a distance ##r##? What is the formula and how would you derive it?
Relevant Equations
Biot-Savart law: ##\displaystyle d\vec B=\frac{I d\vec l\times\hat r}{r^2}##

Lorentz force law: ##\vec F = q\vec v\times\vec B##
The Biot-Savart law gives us the magnetic field created by an electric current. We can calculate the force exerted on a moving charge by this magnetic field using Lorentz's force formula.

But my textbook doesn't address the repulsive or attractive force between like or unlike poles (respectively) of two magnets.
 
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The potential energy of a magnetic dipole ##\vec m## in a magnetic field ##\vec B## is given by
$$
U = - \vec m \cdot \vec B
$$
Use this and take derivatives as usual to find forces and torques .
 
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