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State Gauss's theorem. Obtain an expression for elactric field at any point outside a charged spherical hollow conductor (shell). |
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Answer» Solution :STATEMENT: The total electric flux`(phi)` through anyt closed surface is `1// in _(0)` times the net charge enclosed by the closed surface. Expression for electric intensity at a point outside the uniformly chrged shell  CONSIDER a unifomly chrged thin spherical shell of radius R. Let Q be the charge distributed on the spherical shell. It produces a spherically symmetric electric firld. Let P be a point DISTANT r from the centre of the shell. To determine the FIELD at P, we imagine a Gaussian sphere of radius r with O as its center as shown in the figure. The total electric flux through the Gaussian surface3 is given by, `phi=` Electric field intensity `xx` Area `""because vecE||vecA` According to Gauss theore, we have `phi = (q )/(epsi_(0))` From equation (1) and (2), we have `E xx 4pi r ^(2) =(q)/(epsi _(0))` `E= (q)/(4pi r ^(2) in _(0))` `E = (1)/( 4pi in _(0)) (q)/(r ^(2))` |
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