Three concentricsphereical shells of radii r_(1) ,r_(2)and r_(3) have charge q_(1),q_(2) and q_(3) respectively . If the central sphere is now connected to theearthby a conductingwire , find the final potentials fo the three shells .

Three concentricsphereical shells of radii r_(1) ,r_(2)and r_(3) have

1.	Three concentricsphereical shells of radii r_(1) ,r_(2)and r_(3) have charge q_(1),q_(2) and q_(3) respectively . If the central sphere is now connected to theearthby a conductingwire , find the final potentials fo the three shells .
Answer» Solution :WHENTHE middle SHELL is earthed , CHARGE flowsbetween the shell and the earthits potentialwill be zero . Letq BETHE final charge on themiddle shell . `V_(2) = (1)/(4PI in_(0))((q_(1))/(r_(2)) + (q)/(r_(2)) + (q_(3))/(r_(3))) = 0` `(q_(1)) /(r_(2)) + (q)/(r_(2)) + (q_(3))/(r_(3)) = 0` `(q)/(r_(2)) = - ((q_(1))/(r_(2))+ (q_(3))/(r_(3)))rArrq = - (q_(1) + (q_(3)r_(2))/(r_(3)))` Final potenital of innermostshell is . `V_(1) =(1)/(4 pi in_(0)) ((q_(1))/(r_(1)) + (q)/(r_(2)) +(q_(3))/(r_(3)))` Final potentialof middle shell is `V_(2) = 0` Final potential of outermost shell . `V_(3)= (1)/(4 pi in_(0)) ((q_(1) + q_(2) + q_(3))/(r_(3)))`