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An atom was earlier assumed to be sphere of radius a having a positively charged point nucleus of charge +Ze at its centre . This nucleus was believed to be surrounded by a uniform desity of negative charge that made the atom neutral as a whole.Use this theorem to find the electric field of this atom at a distance r(rgta) from the centre of the atom. |
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Answer» SOLUTION :Let `rho` be the uniform density of negative charge . Wethen have `(4pia^(3)rho)/(3)=Ze` `thereforerho=((3Ze)/(4pia^(3)))` Taking a sphere of radius r (centre at the nucleus) as the Gaussian SURFACE , we have `E(r)xx4pir^(2)=(q)/(epsilon_(0))`.... (i) where , q is the NET charge enclosed by the Gaussian surface . Now `q=(+Ze)+(-rho.(4pir^(3))/(3))` `=Ze-Ze((r^(3))/(a^(3)))` `=Ze(1-(r^(3))/(a^(3)))` Substituting this value of a , in eq . (i) `E(r)=(Ze)/(4piepsilon_(0)r^(2))(1-(r^(3))/(a^(3)))` `=(Ze)/(4piepsilon_(0))((1)/(r^(2))-(r)/(a^(3)))` |
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