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