I haven't found anything that has explained this to my satisfaction. In David Griffiths' Introduction to Electrodynamics, Chapter 5, Section 1, Example 5.3, the author covers the basics of how an electromagnet can lift things. He explains that even though it can appear as though the magnet is somehow lifting an object (i.e. doing work), the Lorentz Force

\(\vec{F}_{\text{magnetic}}=q\vec{v} \times \vec{B}=I\vec{\ell} \times \vec{B}\)​

is not violated. In other words, since the magnetic force is perpendicular to the direction of motion, it cannot do work. The magnetic field merely redirects the work done by the current source. So, in reality, it is the current source (some power supply) that is doing the work necessary to lift things.

This leaves me puzzled as to how a permanent magnet is able to lift an object. Can someone explain that to me?

 

This leaves me puzzled as to how a permanent magnet is able to lift an object.

This is not a good example. One can say that the magnet is not lifting the object since the magnet needs to touch the object and the lifting force is directed through the magnetic field. Just as in the electromagnet.

A better example would be if a magnet and an object place close to each other. Since the magnet can be fixed in place, it cannot do any work. Yet the object is accelerated towards the magnet.

 

This is not a good example. One can say that the magnet is not lifting the object since the magnet needs to touch the object and the lifting force is directed through the magnetic field. Just as in the electromagnet.

A better example would be if a magnet and an object place close to each other. Since the magnet can be fixed in place, it cannot do any work. Yet the object is accelerated towards the magnet.

While your first example could explain how a human being's arm is the source providing the work required to lift an object, analogous to the electrical power supply in David Griffith's Example 5.3, your second example raises the question for me, what is the relevant equation analogous to the Lorentz force equation that would model the effect of using a magnet to "lift" things up?

EDIT: I forgot to mention that in a uniform magnetic field, a magnetic dipole feels no net force (though it does feel a net torque). However, in a nonuniform magnetic field, such as in the fringing magnetic fields around a horseshoe magnet, a magnetic dipole feels both a net force and a net torque. If it feels a net force, there will be an acceleration, and thus movement. Further, in a magnetizable material there are many dipoles across large (compared to the microscopic magnetic dipoles) distances. Each of these portions will feel a different force.

 

While your first example could explain how a human being's arm is the source providing the work required to lift an object, analogous to the electrical power supply in David Griffith's Example 5.3, your second example raises the question for me, what is the relevant equation analogous to the Lorentz force equation that would model the effect of using a magnet to "lift" things up?

I don't know. I wanted to point out that your example is comparable to the electromagnet. The example I provided shows the effect that needs explaining.

Since the object is accelerated, there must be a loss of potential energy from somewhere (1st law of thermodynamics). What is the cause of the potential energy that is transformed?

 

A permanent magnet magnetic field is similar to a gravitational field as far as energy is concerned. They both generate an attractive force which can generate energy when the attracted object moves towards the source of the field. This energy is provided by the fields. If you then forcibly move the object back away from the field you will return the energy to the field.