Two concentric conducting spherical shells have radii R and 2R. The inner shell carries a charge +Q, and the outer shell carries a charge -2Q. Match the following quantities with their correct values.

Question

Two concentric conducting spherical shells have radii R and 2R. The inner shell carries a charge +Q, and the outer shell carries a charge -2Q. Match the following quantities with their correct values. (Take $k = 1/ (4 π ϵ_{0})$ )

List - I	List - II
(P) Electric potential at a distance R/2 from the center	(1) $0$
(Q) Electric potential at a distance 3R/2 from the center	(2) $- \frac{k Q}{3 R}$
(R) Electric potential at a distance 5R/2 from the center	(3) $- \frac{2 k Q}{5 R}$
(S) Magnitude of electric field at a distance 3R/2 from the center	(4) $\frac{4 k Q}{9 R ^{2}}$

TestHub · Accepted Answer

For concentric conducting shells, the potential inside a conductor is constant and equal to its surface potential. The electric field inside a conductor is zero. P: For r < R (inside inner shell), the potential is V R ​ = R k Q ​ + 2 R k ( − 2 Q ) ​ = R k Q ​ − R k Q ​ = 0 . So (P)-(1). Q: For R < r < 2 R (between shells), the potential is V r ​ = r k Q ​ + 2 R k ( − 2 Q ) ​ . At r = 3 R /2 , V 3 R /2 ​ = 3 R /2 k Q ​ − R k Q ​ = 3 R 2 k Q ​ − R k Q ​ = − 3 R k Q ​ . So (Q)-(2). R: For r > 2 R (outside both shells), the potential is V r ​ = r k ( Q − 2 Q ) ​ = r − k Q ​ . At r = 5 R /2 , V 5 R /2 ​ = 5 R /2 − k Q ​ = − 5 R 2 k Q ​ . So (R)-(3). S: For R < r < 2 R , the electric field is due to the inner charge +Q only. E r ​ = r 2 k Q ​ . At r = 3 R /2 , E 3 R /2 ​ = ( 3 R /2 ) 2 k Q ​ = 9 R 2 4 k Q ​ . So (S)-(4).

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