Current and magnetic field in a spherical capacitor

[fabiogn]

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Hello! I have a question on Electromagnetics.

Could anyone check if I am on the right track?
Here is the proposed problem:
Consider a spherically symmetric current distribution, which is radial and corresponds to the slow leak between the plates of a spherical capacitor. Considering now the magnetic flux B caused by this current, choose the right one:

Among the five alternatives there is one that affirms that the magnetic flux is zero outside and inside this capacitor because magnetic field lines never cross and always form closed paths.

Since I cannot figure out how the magnetic poles and field lines regarding the condition above described would be, (it would be like a monopole) I think that this alternative is the right one.

I also have found the text below, which reinforces my point of view:
"because since we have a completely spherically symmetric situation, it could only generate a spherically symmetric magnetic field. But the only possible such fields are one pointing outwards everywhere and one pointing inwards everywhere, both corresponding to non-existent monopoles. So, there can be no magnetic field" Has anyone seen this problem before? Am I right?

Many thanks in advance,
Best regards!
Fabio

 

[Irene Kaminkowa]

We can also regard a miniscule current along the radius from one plate to the other. According to the Biot-Savart law, it creates the magnetic flux Bi. Then, we can easily find the opposite current to create -Bi. And, owing to the spherical symmetry, each elementary magnetic flux has its opposite flux. In the end, their total vector sum is 0.

 

[fabiogn]

Hi Irene, many thanks for your reply!

Let me see if I got it right... So, does it mean that internally there is magnetic flux between the two spherical surfaces of the capacitor?

I really appreciate your help.

 

[Irene Kaminkowa]

There is current from one sphere to the other, but there is no flux. B = 0

 

[fabiogn]

Dear Irene,

Ok! I understood! Many thanks for your help!



Fabio