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
Messages
46
Reaction score
20
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.
 
Physics news on Phys.org
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 .
 
  • Like
Likes MatinSAR and Meow12
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
I was thinking using 2 purple mattress samples, and taping them together, I do want other ideas though, the main guidelines are; Must have a volume LESS than 1600 cubic centimeters, and CAN'T exceed 25 cm in ANY direction. Must be LESS than 1 kg. NO parachutes. NO glue or Tape can touch the egg. MUST be able to take egg out in less than 1 minute. Grade A large eggs will be used.
Back
Top