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A small sphere of radius r_1 and charge q_1 is enclosed by a spherical shell of radius r_2 and charge q_2. Show that if q_1is positive, charge will necessarily flow from the sphere to the shell (when the two are connected by a wire) no matter what the charge q_2 on the shell is. |
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Answer» Solution :The potential of the outer spherical shell `V_2={:("potential DUE to "),("its own charge " q_2):}+{:("potential due to"),("inner charge "q_1) :}` The potential of the inner solid sphere is `V_1={:("potential due to "),("its own charge " q_1):}+{:("potential due to"),("inner charge "q_2) :}` `=1/(4pi epsi_0) (q_1/r_1 + q_2/r_2)` `:. V_1 -V_2 = q_1/(4pi epsi_0)[1/r_1 - 1/r_2] = (q_1(r_2-r_2))/(4pi epsi_0 r_1r_2) = + ve` As positive charge FLOWS from higher potential to lower potential, hence charge will necessarily FLOW solid sphere to spherical shell, when the two are connected by a wire. 
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