# A uniformly charged rotating sphere does not radiate, why not?

• wykk
In summary, the problem describes a spherically symmetric spinning charge distribution with charge Q and angular momentum w, and the question is why the fields are zero. Two possible explanations are given, one involving a constant angular velocity implying a constant electric field and no magnetic field, and the other involving a constant charge density and current density, resulting in a zero magnetic field. Both explanations rely on the time-independent nature of the charge and current distributions, leading to static fields rather than radiation fields.
wykk
Thread moved from the technical forums to the schoolwork forums
The problem says I have a spherically symmetric spinning constant charge distribution of charge Q and angular momentum w; I saw two possible explanations but none of them has made me realize why it is zero, one mentions thata constant w somehow implies a constant E which would mean there is no B and poynting vector would be zero.
Another mentions that the charge distribution rho is constant therefore J the current density is too and B becomes zero but I don't know how to derive an expression that relates B and J

Hi @wykk and welcome to PF.

If this is a homework problem, it should be posted under Introductory Physics Homework with the template provided. Please read the forum homework help guidelines before posting there. I would also strongly recommend posting the exact description of the question as given to you. Providing links to the explanations that you saw would also be helpful as it is possible that you may have misconstrued what you read.

It's because the charge and current distributions are time-independent. Thus you also have static fields. I suppose it's meant that the angular velocity ##\vec{\omega}=\text{const}##.

sophiecentaur
vanhees71 said:
It's because the charge and current distributions are time-independent. Thus you also have static fields. I suppose it's meant that the angular velocity ##\vec{\omega}=\text{const}##.
It's the equivalent of DC passing round a loop of wire; no radiation except at switch on.

vanhees71
Look at the form of the Jefimenko solutions, which are the solutions to electromagnetism in free space. Only the terms that go as ##1/|r-r'|## contribute to the radiation field, all three of these terms are proportional to ##\dot \rho## or ##\dot{\mathbf J}## which are both zero in the case of a spherically symmetric spinning body (or even an axially symmetric one).

vanhees71

## 1. Why doesn't a uniformly charged rotating sphere radiate?

A uniformly charged rotating sphere does not radiate because the electric field lines produced by the rotation of the charges cancel each other out. This cancellation of electric field lines results in no net radiation being emitted from the sphere.

## 2. What is the relationship between the rotation and radiation of a uniformly charged sphere?

The rotation of a uniformly charged sphere does not contribute to any radiation because the electric field lines produced by the rotation cancel each other out. This is due to the symmetry of the charge distribution on the sphere.

## 3. Can a uniformly charged rotating sphere ever radiate?

No, a uniformly charged rotating sphere cannot radiate due to the cancellation of electric field lines. However, if the charge distribution on the sphere is not symmetrical, then it may be possible for the sphere to radiate.

## 4. How does the speed of rotation affect the radiation of a uniformly charged sphere?

The speed of rotation does not affect the radiation of a uniformly charged sphere because the electric field lines always cancel each other out. Therefore, the sphere will not radiate regardless of the speed of rotation.

## 5. What other factors can affect the radiation of a uniformly charged rotating sphere?

The only factor that can affect the radiation of a uniformly charged rotating sphere is the symmetry of the charge distribution. As long as the charges are distributed symmetrically, the sphere will not radiate. However, any asymmetry in the charge distribution can result in radiation being emitted from the sphere.

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