Frame Dependence: Electric and Magnetic Fields Across Inertial Frames

[Starproj]

Homework Statement

Hi,

My professor offered the following question: Is it possible to have an electromagnetic field that appears as a purely electric field in one inertial frame and as a purely magnetic field in some other inertial frame?

Homework Equations

The Attempt at a Solution

I agree that if there is a point charge at rest there exists only electric field lines. And I also agree that if the charge is put in motion that from the frame of the lab there is an electric and magnetic field but from a frame attached to the charge there is only an electric field. But I can't convince myself there could be one frame where there is only an electric field and another frame in which there is only a magnetic field. Can someone point me in the direction of what I am missing? Is this a qualitative or quantitative issue? Am I oversimplifying this?

Thanks in advance!

 

[tiny-tim]

Is it possible to have an electromagnetic field that appears as a purely electric field in one inertial frame and as a purely magnetic field in some other inertial frame?

Hi Starproj!

Hint: what invariants do you know involving E and B?

 

[tomcue]

Hello,

The concept of an electromagnetic field appearing as purely electric or purely magnetic in different inertial frames is a fundamental aspect of special relativity. This phenomenon is known as the electromagnetic field transformation and it is a result of the relative motion between the observer and the source of the field.

In one inertial frame, the observer may see only an electric field because they are at rest relative to the source of the field. However, in another inertial frame where the observer is moving at a constant velocity relative to the source, they will see both electric and magnetic fields. This is due to the fact that the electric and magnetic fields are actually two components of the same electromagnetic field and are therefore inseparable.

The reason for this phenomenon lies in the Lorentz transformation equations, which describe how physical quantities, such as electric and magnetic fields, change between different inertial frames. These equations show that the strength and direction of the electric and magnetic fields are dependent on the relative velocity between the observer and the source.

So, to answer your question, yes, it is possible to have an electromagnetic field that appears as purely electric in one frame and purely magnetic in another frame. This is not a qualitative or quantitative issue, but rather a consequence of the fundamental principles of special relativity. I would suggest further exploring the Lorentz transformations and their implications for electromagnetic fields to gain a deeper understanding of this concept.

I hope this helps clarify the concept for you. Good luck with your studies!