Need for SR to Explain Magnetic Forces?

In summary: See also http://en.wikipedia.org/wiki/Einstein%27s_equation_for_magnetism)In summary, special relativity was invented so that we can describe the fields that cause the force without needing to move away from Galilean relativity. The difference in speeds between the particle and the magnetic field still results in a force, but it is not the same as in a stationary frame.
  • #1
pantheid
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Here's my problem. We know the magnetic force is just F=q(v x B). If we have a stationary charged particle in a magnetic field, it will not feel a force. If we change to a moving frame, the particle now has a velocity, but the idea that it feels a force by changing frames is ridiculous so Einstein invents special relativity. My question is, is that really necessary? The magnetic field now also appears to be moving, so the difference in speeds between it and the particle is still zero, hence no need yet to move away from Galilean relativity. Is my thinking correct or am I missing something?
 
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  • #2
pantheid said:
Is my thinking correct or am I missing something?

It is certainly incorrect. Firstly a magnetic field does not move in the sense that it has a speed. A magnetic field can propagate through electromagnetic waves but that is quite a different concept. What one can have is the source of the magnetic field moving with some speed.

Let's say we have a permanent magnet and a charged particle that are both stationary in a frame ##O##. We then boost to a frame ##O'## that is moving with respect to ##O## at some speed. Then yes in this frame the magnet and the charged particle are still at rest with respect to one another. However the ##v## that appears in the Lorentz force law ##\vec{F} = q(\vec{v} \times \vec{B})## is not the velocity of the charged particle relative to the source of the magnetic field. It is the velocity of the particle relative to the chosen reference frame.

Hence ##\vec{F}\neq 0## in ##O'## whereas ##\vec{F} = 0## in ##O## if one naively follows Galilean relativity since the particle has some speed with respect to ##O'##.
 
  • #3
WannabeNewton said:
the vv that appears in the Lorentz force law F⃗ =q(v⃗ ×B⃗ )\vec{F} = q(\vec{v} \times \vec{B}) is not the velocity of the charged particle relative to the source of the magnetic field. It is the velocity of the particle relative to the chosen reference frame.

Not only that, the ##\vec{B}## that appears in the law is also relative to the chosen reference frame; it changes if you change frames. Also, if the field in frame ##O## is a pure magnetic field, then in frame ##O'## there will be an electric field as well, so the force law has to include a term for that. All this ensures that the actual force felt by the object is invariant under changes of frame--all that changes is how we describe the fields that cause the force.
 
  • #4
pantheid said:
Here's my problem. We know the magnetic force is just F=q(v x B). If we have a stationary charged particle in a magnetic field, it will not feel a force.

If you have a stationary charged particle, and E=0, it will not feel a force, regardless of the value of B. But you forgot to specify the part where E=0, I will assume that this was implied and that you didn't realize you needed to specify this explicitly.

If we change to a moving frame, the particle now has a velocity, but the idea that it feels a force by changing frames is ridiculous so Einstein invents special relativity. My question is, is that really necessary? The magnetic field now also appears to be moving, so the difference in speeds between it and the particle is still zero, hence no need yet to move away from Galilean relativity. Is my thinking correct or am I missing something?

If you happen to know how the E and B fields transform (either by the tensor equations, or the non-tensor version - see for example http://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity) you can compute what happens in the moving frame without solving Maxwell's equations again.

When you start with the E and B fields in your "rest frame" with ##\vec{E}=0## and ##\vec{B}= \vec{B_0}## (using the wiki notation), you'll find that the transformation law that takes E in the rest frame to E' in the primed (moving) frame, i.e. ##E'_{\perp} = \gamma \left( E_{\perp} + v \times \vec{B_0} \right)## gives you a non-zero value for the E field in the moving frame. This should cancel the vxB force, because if the force is zero in one frame it should be zero in all. But I haven't calculated the details.

Now we see the need to specify E - and we note that the value of E is not the same in the moving and stationary frame in general and in this problem in particular.
 
  • #5


Thank you for sharing your thoughts on the need for special relativity to explain magnetic forces. Your understanding of the equation F=q(v x B) is correct; however, special relativity is necessary in this case because it allows us to accurately describe the behavior of charged particles in a magnetic field, regardless of their frame of reference.

In classical mechanics, the laws of physics are the same in all inertial frames of reference. However, when we consider the behavior of charged particles in a magnetic field, we see that their motion is affected by both their velocity and the magnetic field. This means that the laws of physics are not the same in all frames of reference, and special relativity is needed to accurately describe this phenomenon.

One of the key principles of special relativity is that the laws of physics are the same in all inertial frames of reference, but the way we measure time and space may differ. In the case of a charged particle in a magnetic field, the magnetic field may appear to be moving in a different direction and at a different speed in different frames of reference. This means that in order to accurately describe the behavior of the particle, we need to consider the effects of both its velocity and the magnetic field, as well as the differences in how time and space are measured in different frames of reference.

In short, special relativity is necessary to explain magnetic forces because it allows us to accurately describe the behavior of charged particles in a magnetic field, regardless of their frame of reference. I hope this helps to clarify the importance of special relativity in understanding magnetic forces.
 

1. What is special relativity (SR) and how does it relate to magnetic forces?

Special relativity is a theory that explains how the laws of physics behave in inertial frames of reference. In other words, it describes how objects move and interact with each other when they are not accelerating. Magnetic forces are created by the motion of charged particles, and special relativity helps to explain how these forces are affected by the relative motion of different observers.

2. Why is SR necessary to explain magnetic forces?

Without special relativity, the laws of electromagnetism would not be consistent with the principles of relativity. This means that the behavior of magnetic forces would be different depending on the observer's frame of reference, which is not consistent with experimental results. Special relativity helps to unify the laws of electromagnetism and provides a more accurate and consistent explanation of magnetic forces.

3. Can you give an example of how SR explains magnetic forces?

One example is the phenomenon of length contraction. According to special relativity, objects in motion appear to be shorter in the direction of their motion when observed from a different frame of reference. This means that the length of a wire carrying an electric current would appear shorter to an observer moving relative to the wire. This change in length would result in a greater concentration of charged particles, leading to a stronger magnetic force being observed by the moving observer.

4. How does SR affect the equations that describe magnetic forces?

The equations that describe magnetic forces, such as the Lorentz force law, are modified to include terms that account for the effects of special relativity. These modifications take into account the relative velocity between the charged particles and the observer, as well as the length contraction and time dilation effects predicted by special relativity.

5. Are there any other physical phenomena that require the use of SR to be explained?

Yes, special relativity is also necessary to explain other electromagnetic phenomena such as the behavior of electric fields, the propagation of light, and the concept of mass-energy equivalence. It also plays a crucial role in understanding the behavior of high-speed particles and the structure of the universe.

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