1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# A solid non-conducting charged sphere has total charge Q and radius R. If energy stored outside the sphere is V0 joules, then find the self energy of the sphere in terms of V0.

A
56V0
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
B
65V0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
3V0
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
D
V05
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
Open in App
Solution

## The correct option is B 65V0Let us consider a non-conducting sphere charged uniformly with a charge Q on it. We know that, in the outer region of the sphere, electric field is exactly the same as that of a charged conducting sphere. Consider an elemental shell of radius r(>R) and thickness dr as shown in the figure. Field energy stored in the volume of this shell is given as dEout=12ε0E2dV ⇒dEout=12ε0E2×4πr2dr So, field energy stored in the surroundings of this sphere from its surface to infinity can be given as Eout=∫∞R12ε0E2×4πr2dr ⇒Eout=Q28πε0R For a non-conducting sphere, E≠0 at interior points. So, field energy exits in the interior region also. Field energy stored in a elemental shell of radius r(<R) dEin=12ε0(Qr4πε0R3)24πr2dr [∵E=Qr4πε0R3] Integrating on both sides, we get Ein=R∫0(Q2r38ε0R6)dr ⇒Ein=Q240πε0R Self energy of solid non-conducting sphere is equal to the total field energy given by Eself=Ein+Eout=35KQ2R where, K=14πε0 Given, Eout=V0=KQ22R ∴EselfEout=65 ⇒Eself=6V05 Hence, option (b) is the correct answer.

Suggest Corrections
1
Join BYJU'S Learning Program
Join BYJU'S Learning Program