Why magnetic field doesn't do any work on moving charge? As we know the Lorentz force $F=qv\times B$ never does work on the particle with charge $q$. But it does work on a dipole.
My question is, doesn't a moving charge behaves like a dipole? I mean an electron moving around nucleus behaves like magnetic dipole then why doesn't a moving charge behaves like a magnetic dipole?
 A: You already know why the magnetic field does no work on a moving charge: because the Lorentz force law says so. There are, in effect, two different force laws for the magnetic field: one that applies to moving charges, and one that applies to point dipoles (and the latter can do work, when the field is non-uniform).
Your question seems to be about the inconsistency between the two scenarios. We know that a point magnetic dipole can be modelled as the limit of a current loop as the area goes to zero, while keeping the product of the area and current constant (and assuming that the charged particles flowing through the loop don't have any intrinsic magnetic dipole moment). But we know that the magnetic field doesn't do any work on the charges flowing through the current loop. How, then, is it possible for the magnetic field to do work on a point magnetic dipole? Shouldn't the limit of zero work on current loops as their areas go to zero be zero work, instead of the nonzero work that is done on point dipoles?
To resolve this paradox, we need to analyze the scenario only in terms of observable quantities. It turns out that "which force is actually doing the work?" is not observable, so the paradox goes away.
Suppose a rigid, initially stationary current loop is placed in a non-uniform external magnetic field. The current loop will experience a net force because the Lorentz force on one side of the loop will not be equal and opposite to the Lorentz force on the other side of the loop (due to the non-uniformity). The net force will be approximately $\nabla(m \cdot B)$ where $m$ is the magnetic dipole moment of the loop. As a result of this net force, the loop will accelerate (and, therefore, acquire kinetic energy). It can be shown that the movement of the loop will be in the direction that will tend to reduce the total amount of energy stored in the magnetic field (which is proportional to $\int B^2 \, \mathrm{d}^3x$, where $B$ is the sum of the external field and the field generated by the loop itself). Thus, there is a transfer of energy from the $B$ field to the loop's kinetic energy.
In the limit where the radius of the loop goes to zero, the same is true. The magnetic field loses energy, and the point dipole gains kinetic energy. There is no discontinuity.
The apparent paradox only arises when we analyze more deeply what is actually happening to the rigid current loop: the magnetic force is exerted on the current carriers and does no work on them directly; work is done by the electric forces that maintain the rigidity of the loop and keep the electrons from leaving the wire. For a point dipole, there are no actual current carriers, so there is nothing to analyze and we just say the magnetic force does the work directly.
When calculating any observable having to do with the point magnetic dipole, we can do it by taking an appropriate limit as the area of a current loop goes to zero. Since "which force is actually doing the work?" is not a question that is phrased in terms of observables, there is actually no quantity to take the limit of in this case.
A: An (non-zero) electric charge is Lorentz-invariant. So in motion an (non-zero) electric charge cannot become a dipole since a dipole has 2 opposite charges, therefore has total charge zero. If it could become a dipole during motion, it would violate Lorentz-invariance of the charge.
EDIT
The best known experiment of a magnetic dipole in a (inhomogeneous) magnetic field is the Stern-Gerlach experiment where silver atoms are heated, so they start moving due to the heat into a (previously set up) inhomogeneous magnetic field where they experience a force, so indeed on the magnetic dipoles of the silver atoms work is done.
But when the silver atoms are not heated, they stay at rest, they already have a magnetic dipole even if they stay at rest. So one could say, they have a magnetic dipole right from the beginning and in particular there is no charge.
They is no charge in this experiment that gets transformed into magnetic dipoles due to their motion.
One could even exert the inhomogeneous magnetic field on the silver atoms at rest, work would be done on their magnetic dipoles too. Motion is not necessary for this.
In the experiment the silver atoms are just moved to make a sucessful observation of their magnetic dipoles and their associated spin.
So this a completely different physical experiment as a single charge moving in magnetic field (Lorentz force experiment).
By the way, one can make the experiment with a permanent magnet in a inhomogeneous magnetic field. This permanent magnet constitute a magnetic dipole and will feel a force and work can be done on it.
But, that is important, there is no charge at all around.
A: In a particle accelerator, the charges are deflected sideways by magnets and thus forced into a circular path. What happens in the process?
Firstly, permanent magnets could be used for this and they would not lose their magnetic field nor would it weaken. Secondly, the particles emit electromagnetic radiation in a narrow cone forwards and slightly sideways out of the ring.

Source
What happens in the process? We have particles with kinetic energy (previously accelerated by electric fields) and their magnetic dipoles are aligned in the magnetic field. It looks like the particles will respond by emitting photons. And in the process, the particles - as long as they are exposed to the external magnetic field - are forced into a circular-like path. They discontinuously lose kinetic energy (converted into photons) and slow down.
The magnet only serves as a kind of catalyst or like a spring. When the particles pass, the magnetic field of the magnet and the magnetic dipoles of the particles interact. After the passage, the magnetic field of the magnet is just as strong as before the passage.
My question is, doesn't a moving charge behaves like a dipole? A charged particle is a permanent magnetic dipole. The value of the magnetic dipole of the electron is a constant (see NIST).
