A conducting spherical shell of rad. R is placed concentrically inside another similar shell of rad. 2R. The inner shell has a charge Q. If it's connected to the outer shell by a coducting wire , find loss in elec.energy .....
(A) zero (B) Q2/(8 \pi \varepsilono R)
(C) Q2/(4 \pi \varepsilono R) (D) Q2/(16 \pi \varepsilono R)
Pls. post soln also. I have a doubt on the soln. given.
1treat first inside shell as capacitor and apply find the energy using .5Q*Q/C. Then find the charges after distribution by applying potential on the both surface. Then once again use the capacitor formula for both the shells, then find the diff.
11my doubt is that in Ui do we also consider the charge induced on the outer shell ???????????
11I didnt understand the soln given (although their ans & mine is the same)
the soln says....
Ui = (1/2) Q2/(4 pi Eo R) -- Q2/(4 pi Eo (2R) ) + (1/2) (-Q)2/(4 pi Eo (2R) ) + (1/2) Q2/(4 pi Eo (2R) )
= (1/2) Q2/(4 pi Eo R)
Uf = (1/2) Q2/(4 pi Eo (2R) )
Loss = | Uf - Ui | = Q2/(16 pi Eo R)
what i did was...
Ui = (1/2) Q2/(4 pi Eo R) [ i.e. U = (1/2) Q2/C ; C = 4 pi Eo R ]
Uf = (1/2) Q2/(4 pi Eo (2R) ) [ i.e. U = (1/2) Q2/C ; C = 4 pi Eo (2R) ]
Loss = | Uf - Ui | = Q2/(16 pi Eo R)