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A system consists of a uniformly charged sphere of radius R and a surrounding medium filled by a charge with the volume density rho=alpha/r , where alpha is a positive constant and r is the distance from the centre of the sphere. Find the charge of the sphere for which the electric field intensity E outside the sphere is independent of R. |
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Answer» `alpha/(2epsilon_0)` `int_0^r Eds=1/epsilon_0 int_0^r rho(r)DV` `rArr E4pir^2 =1/epsilon_0 (q+int_R^r alpha/r (4pir^2)DR)` `rArr E4pir^2 = ((q-2pialphaR^2))/epsilon_0+(4pialphar^2)/(2epsilon_0)` The intensity E does not depend on R if `(q-2pialphaR^2)/epsilon_0=0` or `q=2pialphaR^2` |
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