# Why are diamagnetic materials repelled when the B field is not changing?

In one of the texts I'm reading, Halliday explains diamagnetism without quantum mechanics by describing an electron circling in a loop like a wire. Initially the electrons moving clockwise and counterclockwise are equal and there is no magnetic dipole moment. If a magnet is brought closer to the loop, regardless of which of two directions an electron electron orbits, Lenz's law says a B field will oppose this increase in flux using the right hand rule and the magnetic fields in the plane of the orbit cancel while perpendicularly they add so that the atom is repelled. The force upward in orientation b in the figure is increased while the force downward in orientation d is decreased. I understand this is a simplification, but why would the repulsion remain when the magnet is stationary for instance to levitate a frog as seen in the text and on wikipedia's page.

The fictitious current loops are permanent in that the current in a loop does not change with time unless an external influence is present.

In this case the external influence is an external magnetic field being switched on.
When the external magnetic field is changing an electric field is induced in the loop (Faraday) which accelerates (either positive of negative) the electron which is moving in the loop.

When the external magnetic field reaches a constant value then there is no longer an electric field accelerating the electron and the electron now moves around the loop at its new speed.

So the external magnetic field in changing from zero to a constant value has changed the speed of an electron moving in a loop from a constant initial value to a constant final value which is either larger or smaller than the initial value depending on the sense of the electron's rotation relative to the external magnetic field direction.

As is explained in the passage this results in some electrons moving slower and some electrons moving faster thus altering their magnetic dipole moments which results in a net downward magnetic moment if there has been an upward external field switched on.

You can demonstrate the levitation of a pencil lead at home.

• So this magnetic moment doesn't serve to produce a torque in the traditional sense. These faster moving e's with a higher orientation energy will experience a net $F_B=Bi(2\pi r)$ whereas before it was magnetically neutral. It makes sense now. – user5389726598465 Aug 19 '17 at 10:02

A picture utilizing forces is needed to understand the dynamics of a system. However, if you are merely interested in the "equilibrium-state", an energy consideration might be much simpler.

The energy of a magnetic moment inside a B-field is given by $E = -\vec \mu \cdot \vec B$. Therefore, if both vectors point into the same direction, the energy is minimized at the maximum of the B-field. In contrast, if both vectors point into opposite direction, the energy is minimized at the minimum of the B-field (assuming that the field can not change sign). You can check, that this is consistent with the directions of forces in your pictures above.

So if the magnetic moments sits at the spot of minimal energy, "it doesn't have a tendency" to move out of it, because this will cost energy. Hence, at this spot the forces acting on the magnetic moment will compensate themselves: E.g. gravity and magnetic interactions.