Electric field is zero at center of cavity?

[positron]

Does an electric field exist in the center of a cavity inside a sphere? Can I just apply Gauss's law and say that because no charge is enclosed, the electric field is zero? If not, why can Gauss's law not be applied?
Thanks,
positron

 

[vanesch]

Does an electric field exist in the center of a cavity inside a sphere? Can I just apply Gauss's law and say that because no charge is enclosed, the electric field is zero? If not, why can Gauss's law not be applied?

Gauss' law can be applied ; but it doesn't say that the E-field is 0, it only says that the flux of the E-field through a closed surface must be 0. So as long as one part is "incoming" and another part is "outgoing" then that's still ok.

cheers,
Patrick.

 

[robphy]

Gauss' Law only tells you about the flux of the electric field vectors on that Gaussian surface... You need to appeal to additional information, e.g. symmetries of the field and/or of the Gaussian surface, to deduce information about the field vectors themselves (i.e., derive an expression for E on that surface). In other words, for your problem, you have to argue [say, using Gauss and symmetry... and possibly a sequence of Gaussian surfaces] that zero enclosed charge implies zero electric field at the center.