If I have a charge outside of a metal sphere, how do I calculate the flux through the surface of the sphere? Thank you so much!
its zero (by gauss law) else do the integral
NO wait...if your charge is placed in front of that sphere , then that sphere will be charged by induction and that charge gained by induction will spread across sphere than you can apply electric flux= charge/ epsilon or \[\int\limits_{initial}^{final} E.ds=\frac{ Q }{ \epsilon }\]
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Consider the field lines created by the field of the charge outside the sphere. Equal amount of field lines will LEAVE the sphere as compared to those ENTERING the sphere at any finite time. So, the total flux through the sphere is \[E.dA + (-E.dA)\] = 0. For more info check out http://physics.info/law-gauss/
Thank you guys. I haven't been on this site lately so didn't have a chance to thank you!
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