1.

Show that the electric field at the surface of a charged conductor is given by `vecE = (sigma)/(epsi_(0)) hatn` , where `sigma` is the surface charge density and `hatn` is a unit vector normal to the surface in the outward direction .

Answer» Electric field at a point on the surface of charged conductor , `E = (1)/(4 pi epsi_(0)) (Q)/(R^(2))` .
Let , consider charged conductor as a sphere of radius R. if `sigma` is in surface density , then
`Q = 4 pi R^(2) sigma`
`E = (1)/(4 pi epsi_(0)) = (4 pi R^(2) sigma)/(R^(2)) = (sigma)/(epsi_(0))`
`vecE = (sigma)/(mu_(0)) hatn` ... where n is a unit vector normal to the surface in the outward direction .


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