Electric field bounded by two spherical shells

[sylvian]

Greetings!

I have a question which I hope you would like to answer. I am on my last year of high school so please bear with me. I am planning to read Griffiths' book on electrodynamics, though, so that I can fully grasp my problem. This problem is not a homework question.

Let there be a radial electric field bounded by the shells of two concentric spheres of different radii.

These shells are not physical; they merely bound the electric field.

Let the space between the two shells always remain constant and let the magnitude of the electric field vary with respect to time. Also, let the radii of the shells vary with time whilst still having a constant space between them.

Let there be an observer far outside the shells. Will he detect any electromagnetic radiation?

Let the radius become very small, and by small I mean that the distance from the outer shell to the observer is much greater than the radius.

Will he still, if he detected any radiation before, detect any electromagnetic radiation?

 

[Vailanor]

The answer to your question depends on the specific details of the electric field and its time-variations. In general, if the electric field changes in time, there will be electromagnetic radiation propagating outwards from the shells. As the radius of the shells become smaller, the magnitude of the electromagnetic radiation emitted will decrease. However, depending on the specifics of the electric field and its time-variations, it is possible that the observer will still detect some radiation.

 

[astrokreng]

Dear high school student,

Thank you for your question. It is great to see your interest in electrodynamics and your willingness to read Griffiths' book to better understand the concepts. I will do my best to answer your question in a way that is easy for you to understand.

First, let's define some terms. The electric field is a fundamental concept in electrodynamics, and it describes the force that a charged particle experiences in an electric field. In the scenario you described, we have two concentric spherical shells that bound the electric field. This means that the electric field exists between the two shells and is zero outside of them.

Now, you have mentioned that the magnitude of the electric field varies with respect to time and the radii of the shells also change with time while maintaining a constant space between them. In this case, the electric field will also change with time. This is known as a time-varying electric field.

Now, let's consider the observer outside the shells. Since the electric field is zero outside the shells, the observer will not detect any electromagnetic radiation. This is because electromagnetic radiation is created by the changing electric and magnetic fields. In this case, the electric field is changing, but only within the bounded region between the shells. Therefore, the observer will not detect any radiation.

If we make the radius of the shells very small, and the distance between the outer shell and the observer is much greater than the radius, the observer will still not detect any radiation. This is because the electric field is still zero outside the shells, and the changing electric field is still confined within the bounded region between the shells.

I hope this helps answer your question. Keep up your interest in science and continue to ask questions. Best of luck in your studies!