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State Gauss theorem in electrostatics. Prove that no electric field exists inside a hollow charged sphere. |
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Answer» Solution :For Gauss theorem , refer under the heading " Chapter At A GLANCE "Consider a hollow CHARGED conducting sphere of radius R and having charge Q .To find electric field at a point P inside the shell , consider a sphere through point P and having centre O, i.E. r= The electric flux through the Gaussian surface ` ""phi _in = oint oversetto E . hat n ds = E 4 pi r^(2) ` According to Gauss theorem, TOTAL electric flux should be ` ""phi _in =(1)/( in _0)` (charged enclosed )= 0 [Since the Gaussian surface is not enclosing any charge] Thus ` ""phi_in = E. 4 pi r^(2)=0"" ...(II) ` [Since the Gaussian surface is not enclosing any charge] Thus ` phi _in =E. 4 pi r^(2) =0 ` `rArr ""E=0 ` Hence , no electric field exists inside a hollow charged sphere. 
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