A solid metal sphere of radius R having charge q is enclosed inside the concentric spherical shell of inner radius a and outer radius b as shown in figure. The approximate variation electric field E as a function of distince r from centre O is given by:
(A)(see structure)
(B)(see structure)
(C)(see structure)
(D)(see structure)✓ Correct
Answer: (D)
Solution
The inner sphere is metallic, so its charge lies on its surface and the field is zero for r<R. Immediately outside its surface the field jumps to R2kq and then falls as r2kq up to the inner face of the shell. Within the conducting material of the shell, a<r<b, the field is zero again: charge −q is induced on the inner face and +q appears on the outer face so that the metal carries no field. Beyond the shell the charge enclosed is once more q, so the field restarts at b2kq at r=b and decays as r2kq. The graph is therefore zero from the centre to R, an inverse-square fall from R to a, zero from a to b, and an inverse-square fall beyond b.
JEE Main · 2021 · 26 Aug 2021 · Shift 1 · Single correct option