# Why do magnetic fields act on moving free charges?

I can understand why ferromagnets create a magnetic field around them, because of the orientation of the magnetic spin of their electrons, and how other permanent magnets can respond to that magnetic field, because the material is magnetized.

However, why does a moving charge get deflected by a magnetic field? It's not like it's magnetized at all, I think, and it's even more counter-intuitive that the force exerted on the particle in question is perpendicular to the magnetic field, unlike what happens in electric or gravitional fields.

Why do free charges and magnetized objects behave differently in a magnetic field, and why do moving free charges feel the field at all?

• Think about it, doesn't a moving charge produces a magnetic field? Is it so strange than it has interactions with external magnetic fields? – Run like hell Dec 14 '16 at 17:04
• @Runlikehell, yes, to me it is weird, that's why I'm asking the question. Maybe the problem is that we never play with moving elementary charges in a magnetic field when we are kids, but we do feel gravity and also play with charged balloons, that's why I find electrostatics and gravity intuitive, but not magnetism outside permanent magnets. – ChemiCalChems Dec 14 '16 at 17:06
• @Runlikehell I'll make this clear. I know a moving charge produces a magnetic field too, if not, it wouldn't interact with other magnetic fields. The question is why? – ChemiCalChems Dec 14 '16 at 17:10
• Are you sure that "why" is the right question to ask? – fffred Dec 14 '16 at 17:28
• As you see, "Why?" is a hard question to answer because we don't know what will satisfy the question. For example, can you answer the question "Why do like charges repel?" One answer is "Coulomb's Law". Another is "Nobody knows" another is "Physics provides a description of nature, not an explanation." – garyp Dec 14 '16 at 17:35

The magnetic B-field is defined in terms of the Lorentz force exerted on a moving charged particles, such that a particle moving in an electromagnetic field experiences a force of $q\vec{E} +q\vec{v}\times\vec{B}$ (see here).

When considered in the context of special relativity, there is only an electromagnetic field. What we choose to define as electric or magnetic fields are simply frame-dependent manifestations of that field - hence the velocity term in the Lorentz force.

Starting with a basic idea of how electric fields work for charged particles, you can demonstrate that a magnetic component to the Lorentz force is required that acts perpendicularly to the velocity, using this type of argument, which I won't cut and paste here.

As you has stated correctly, charged particles have a magnetic dipole moment, you called it magnetic spin. The point is that a stationary electron under the influence of a magnetic field will be aligned for one time only. For a moving charge his magnetic dipole moment will be aligned and due to gyroscopic effect the electron will be declined (deflected).

A deflection is an acceleration and it is known that in this case photons will be emitted from the electron. Since photons carrying momentum happens a disalignment of the magnetic dipole moment to the external field. And the game starts again: Alignment, deflection, photon emission, disalignment. The electron loose kinetic energy, the trajectory is a spiral path and more than this, the spiral is made from tangerine slices.

The action of an external magnetic field is like the action of a spring. The external field does not contribute energy to the deflections in sum.

With the above said it is clear why a moving parallel to the external magnetic field electron does not get deflected. Simple the gyroscopic effect does not works.

You may find the answer to your question in a recent work that explains the magnetic force as purely electrostatic due to electric force interaction between moving current charges, the paper title is "Two New Theories for the Current Charge Relativity and the Electric Origin of the Magnetic Force Between Two Filamentary Current Elements". The explanation has been proved by deriving the the magnetic force law and Biot-Savart law using the basis of electric forces as specified in the electromagnetic theory for constant currents. The explanation is too long to be described here. You can read the paper at http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=7546893 . In short, electric currents even those produced by moving charges are equivalently represented by charges moving at the speed of light. By analyzing the electric field spreading through the space by these moving charges, it is found that they alternate from positive to negative and negative to positive due to the switching between the moving negative and positive charges to create the current. By applying Gauss law, positive and negative charges are found at the electric field discontinuity locations. These charges interact with the moving current charges of other elements generating the magnetic force observed due to the existence of the source current element. These discontinuity charges produce a zero net force on a static charge while produce the observed magnetic force on a moving charge.

## protected by Qmechanic♦Dec 31 '16 at 8:13

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