Charge Sphere Radiation & E Field: Griffiths Explained

[cragar]

In Griffiths he talks about a charged sphere and that if it pulsed in an out i would not radiate.
He says if you draw a Gaussian surface around it the E field doesn't change, as long as you are outside of it. But wouldn't the charges accelerate and you would think they would radiate. But maybe the field cancels in a way as to prevent this.

 

[tiny-tim]

hi cragar!

if the sphere is always spherically symmetric, then so must its field be …

so if you draw a big sphere round it, the flux density across it must be uniform (at any time) …

since the total flux (at any time) must be zero (Gauss' Law), that means the uniform flux density (at any time) must be zero, ie no flux

if, alternatively, the sphere has a dipole pulsation, then again the total flux will be zero, but now the flux density will be non-uniform, so there can (and will) be a flux

(same for an accelerating charge … total flux zero, flux density non-uniform and non-zero)​

 

[jtbell]

if, alternatively, the sphere has a dipole pulsation, then again the total flux will be zero, but now the flux density will be non-uniform, so there can (and will) be a flux​

...inwards at some locations on the sphere and outwards at other locations.

(Just to expand your statement a bit. I know from experience that some students need to be reminded that "total flux = 0" is not the same thing as "flux = 0 everywhere".)​

 

[cragar]

ok thanks for your answers

 

[sardar]

Griffiths' explanation is correct. The key concept here is that of conservation of energy. In order for an object to radiate energy, it must experience a change in its energy state. In the case of a charged sphere that is pulsing in and out, the charges are not actually changing their energy state, but are simply moving back and forth within the sphere. Therefore, no radiation is produced.

Additionally, the E field inside the Gaussian surface is constant because the charges are evenly distributed on the surface of the sphere. This means that the electric field lines are equally spaced and cancel out each other's effects. As a result, there is no net change in the electric field outside the sphere, and thus no radiation is produced.

It is important to note that this explanation only applies to a perfectly spherical, evenly charged sphere. In reality, there may be some irregularities in the charge distribution or some external forces acting on the sphere that could cause it to radiate. But in the ideal case described by Griffiths, the charges will not radiate as they are not experiencing a change in their energy state.