# Point Charges & Magnetism: Relativity's Role

• lovetruth
In summary: This means that it only appears to exist because of the way we perceive motion and space. In reality, there is no fundamental force of magnetism, but rather it is a consequence of relativity. However, this does not mean that magnetism is not a real phenomenon. It is just not a fundamental force like the electric force. Additionally, magnetism arises due to the length contraction of extended charged objects, which increases the charge density and therefore creates a magnetic field. This effect can also be observed in point charges, as they can still experience changes in charge density and length contraction. Ultimately, whether or not a particle experiences magnetism is
lovetruth
Magnetism is said to arise due to relativity. When an extended charged object move, length contraction occurs which increases the objects charge density thus increasing electric field which is then perceived to be caused by magnetism (if we do not account for relativity). Thus, magnetism is a relativistic effect.

My Question is : Will point charges show magnetism as they do not have any length which can contract?

lovetruth said:
Magnetism is said to arise due to relativity. When an extended charged object move, length contraction occurs which increases the objects charge density thus increasing electric field which is then perceived to be caused by magnetism (if we do not account for relativity). Thus, magnetism is a relativistic effect.

My Question is : Will point charges show magnetism as they do not have any length which can contract?

Your explanation is not quite right. The magnetic field appears in a moving frame to counter-act the change in the electric field, so all observers will agree on the path of a charge in a field.

From the article

So observers in the two frames will agree on the rate at which the particle accelerates away from the wire, but one will call the accelerating force magnetic, the other electric. We are forced to the conclusion that whether a particular force on an actual particle is magnetic or electric, or some mixture of both, depends on the frame of reference—so the distinction is rather artificial.

Yes, a moving point charge has a magnetic field.

Mentz114 said:
Your explanation is not quite right. The magnetic field appears in a moving frame to counter-act the change in the electric field, so all observers will agree on the path of a charge in a field.

From the article

Yes, a moving point charge has a magnetic field.

Please elaborate wat u mean by " counter-act the change in the electric field, so all observers will agree on the path of a charge in a field." I didnt quite get it.

lovetruth said:
Please elaborate wat u mean by " counter-act the change in the electric field, so all observers will agree on the path of a charge in a field." I didnt quite get it.

Suppose there's an experiment where an electron is slung through an electric field, which deflects it so it hits a certain spot on a screen.

An observer, moving inertially relative to the lab, would see the electric field as changed, and therefore would not expect the electron to hit the same spot, if they consider only the electric field. But they must see the electron hit the same spot as the observers in tha lab, and indeed they do. The reason is that a magnetic field would also be present for the moving observer, and this (in their calculations) would do just enough to steer the electron through the hole. It is almost as if the magnetic field is there to ensure that no causal paradox happens.

Mentz114 said:
Suppose there's an experiment where an electron is slung through an electric field, which deflects it so it hits a certain spot on a screen.

An observer, moving inertially relative to the lab, would see the electric field as changed, and therefore would not expect the electron to hit the same spot, if they consider only the electric field. But they must see the electron hit the same spot as the observers in tha lab, and indeed they do. The reason is that a magnetic field would also be present for the moving observer, and this (in their calculations) would do just enough to steer the electron through the hole. It is almost as if the magnetic field is there to ensure that no causal paradox happens.

The link i have provided proves that : Magnetism is just a Relativistic effect and not a fundamental force like Electric force; just as centrifugal is a pseudoforce. Now, magnetism arises due to length contraction of extended charged bodies which increases charge density thus leading to magnetism. Electron is an extended body i.e. it has finite volume but what about a point charge? It is just a point and cannot be squeezed further.

lovetruth said:
The link i have provided proves that : Magnetism is just a Relativistic effect and not a fundamental force like Electric force; just as centrifugal is a pseudoforce.

I'm afraid it doesn't. One statement is "a moving charge produces a magnetic field". Another statement is "Given an arbitrary E and B field, there always exists a frame where the field is purely electric." Statement 2 does not follow from Statement 1.

Mentz114 said:
Your explanation is not quite right. The magnetic field appears in a moving frame to counter-act the change in the electric field, so all observers will agree on the path of a charge in a field.

Every inertial observer will agree with the first and higher derivatives of the path of the charge, but not every observer will agree on how much distance the charge traveled over time. Nor will they agree on the electric and magnetic components of the field. Nor will they agree on the angle between the acceleration $\mathbf{x}''$ of the charge and the velocity $\mathbf{x}'$ of the charge. The acceleration $\mathbf{x}''$ of the charge is the same for all inertial observers, but the velocity $\mathbf{x}'$ of the charge is the same only for co-moving inertial observers.

lovetruth said:
Now, magnetism arises due to length contraction of extended charged bodies which increases charge density thus leading to magnetism.

Whether a particle experiences a gain of magnetism, or a loss, is relative to the observer.
Whether a particle experiences a gain of charge density, or a loss, is relative to the observer.
Whether a particle experiences a gain of length contraction, or a loss, is relative to the observer.

...if Lorentz ether theory is not correct.

I'm afraid it doesn't. One statement is "a moving charge produces a magnetic field". Another statement is "Given an arbitrary E and B field, there always exists a frame where the field is purely electric." Statement 2 does not follow from Statement 1.

The concept of magnetism is only invoked when relativistic effect like length contraction are ignored. When Maxell wrote electromagnetic equation, he didn't kno about relativity. Thus, magnetism was used as a scapegoat to explain the relativistic phenomena.

kmarinas86 said:
Whether a particle experiences a gain of magnetism, or a loss, is relative to the observer.
Whether a particle experiences a gain of charge density, or a loss, is relative to the observer.
Whether a particle experiences a gain of length contraction, or a loss, is relative to the observer.

...if Lorentz ether theory is not correct.

Lorentz ether theory is correct excluding the concept of ether. Lorentz transformation is correct and is incorporated in SR.
So there is no doubt in the 3 statements u stated. Remove the word 'whether' as the 3 statements r absolutely correct.

kmarinas86 said:
Every inertial observer will agree with the first and higher derivatives of the path of the charge, but not every observer will agree on how much distance the charge traveled over time. Nor will they agree on the electric and magnetic components of the field. Nor will they agree on the angle between the acceleration $\mathbf{x}''$ of the charge and the velocity $\mathbf{x}'$ of the charge. The acceleration $\mathbf{x}''$ of the charge is the same for all inertial observers, but the velocity $\mathbf{x}'$ of the charge is the same only for co-moving inertial observers.

Could you please elaborate more on the last affirmations (preservation of the acceleration in a change of inertial frame) or suggest references to learn more about these items?

## 1. What is a point charge?

A point charge is an idealized concept in physics that represents a particle with a single, concentrated electrical charge. This charge is assumed to be infinitely small in size and located at a single point in space.

## 2. How do point charges interact with each other?

Point charges interact through the electromagnetic force, which is mediated by the exchange of virtual photons. Like charges repel each other, while opposite charges attract.

## 3. What is the role of relativity in point charges and magnetism?

Relativity plays a crucial role in understanding the behavior of point charges and magnetism at high speeds. It explains how electric and magnetic fields can appear to transform into each other depending on the observer's frame of reference.

## 4. Can point charges and magnetism be explained using classical mechanics?

Yes, classical mechanics can adequately describe the behavior of point charges and magnetism at low speeds. However, at high speeds, the predictions of classical mechanics do not match experimental observations, and the principles of relativity must be used instead.

## 5. How do point charges and magnetism affect each other?

Point charges and magnetism are closely related, as moving charges create magnetic fields and changing magnetic fields can induce electric fields. This relationship is described by Maxwell's equations, which unify electricity and magnetism into a single electromagnetic force.

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