Of course an electron produces an electric field, whether placed in a magnetic field, or not; it suffices to look at Maxwell’s equations!

Stam Nicolis Maxwell's equations might be sufficient for this, but they might not be. They are not for electrons in atomic orbitals, which do not continuously radiate as Maxwell's equations seem to indicate they will.

It doesn’t matter. An electric charge, classical or not, produces an electric field, aa can be seen by computing the corresponding quantities in the appropriate framework. A free electron prcecesses, when in an external magnetic field and produces an electric and a magnetic field in fact. One way to see this is by dolving Maxwell’s equations.Another is by solv8ng the quantum problem.

Dear Arbab:

At the first, and as you know that Protons and neutrons which are the constituents of atomic nuclei possess the quantum mechanical property of spin which has magnitude and direction. We can imagine these particles as if they were small spinning tops. As a result of spin, the nuclear particles act as small bar magnets. Inside the nucleus, these small magnets associated with the nucleons (protons and neutrons) line up so as to cancel each other's magnetic fields. However, if the number of nucleons is odd, the cancellation is not complete, and the nucleus possesses a net magnetic moment. Therefore, nuclei with an odd number of nucleons behave as tiny magnets. Hydrogen, which has a nucleus consisting of a single proton, does, of course, have a nuclear magnetic moment. The human body is made of mostly water and other hydrogen-containing molecules. Therefore, MRI images of structures within the body can be most effectively produced using the magnetic properties of the hydrogen nucleus. Our discussion will be restricted to the nuclear magnetic properties of hydrogen.

Normally, the little nuclear magnets in bulk material are randomized in space as is shown in Fig.(a) and the material does not possess a net magnetic moment (M=0). The nuclear magnets are represented as small arrows. However, the situation is altered in the presence of an external magnetic field. When an external magnetic field is applied to a material possessing nuclear magnetic moments, the tiny nuclear magnets line up either parallel or antiparallel with the magnetic field as shown in Fig. (b). The direction of the external magnetic field is usually designated as the z-axis. As shown in the figure, the x-y plane is orthogonal to the z-axis. Because the nuclear magnets parallel to the field (+z) have a somewhat lower energy than those that are antiparallel (-z), more of the nuclei are in the parallel state than in the antiparallel state. In an external magnetic field, the assembly of parallel/antiparallel nuclear spins as a whole has a net magnetic moment M that behaves as a magnet pointing in the direction of the magnetic field.

The energy spacing ΔEm between the parallel and antiparallel alignments is

ΔEm=γhB2π

Here B is the externally applied magnetic field, h is the Planck constant as defined earlier, and γ is called gyromagnetic ratio which is a property of a given nucleus. Typically the strength of magnetic fields used in MRI is about 2 tesla (T). (By comparison, the strength of the magnetic field of the Earth is on the order of 10-4T.)

The discrete energy spacing ΔEm, between the two state makes this a resonant system. The frequency corresponding to the energy difference between the two states is called the Larmor frequency and is given by

fL=ΔEmh=γB2π

The gyromagnetic ratio γ for a proton is 2.68×108T-1sec-1. Magnetic fields used in MRI are typically in the range 1 to 4 T. The corresponding Larmor frequencies are about 43 to 170 MHz. These frequencies are in the radio frequency (RF) range, which are much lower than X-rays and do not disrupt living tissue.

If by some means the magnetic moment is displaced from the field, it will precess (rotate) around the field as a spinning top precesses in the gravitational field of the Earth. The frequency of precession is the Larmor frequency. The displacement of the magnetic moment is due to a reversal of alignment for some of the individual nuclear magnetic moments from parallel to antiparallel alignment. A displacement of 90° corresponds to equalizing the population of the spin up and spin down states. To reverse the alignment of antiparallel spins requires energy which must be supplied by an external source.

# For more details please check this valuable articles about the topic at:

https://www.sciencedirect.com/topics/computer-science/larmor-frequency.

I hope it will be helpful...

With my best regards...