a rubber balloon is given a charge q distributed uniformly over its surface is the field inside the baloon zero everywhere if the balloon does not have a spherical surface?
Answers
Answer:
Explanation:
We conider a uniform charge distribution over the surface of a balloon. Two cases : spherical ballon, or non-spherical balloon.
Spherical ballon : we can use spherical symmetry to say that the electric field is along r axis, and depends only on r coordinate. Then integrate Gauss over a sphere of radius r inside the balloon give E=0.
Non-spherical ballon : no more spherical symmetry!! So E can depends on the 3 coordinates, and the direction is a priori not along the r axis. So integrating Gauss over a sphere of radius r (the sphere being totally inside the ballon, thus no charge inside the sphere) will give us : integral(E.dS)=integral(E_r)=0. Thus E_r (the composante of E along the r axis) can be non-zero at some points (or even everywhere), while the integral remaining 0.