Three point charges are kept at various places of a cube. Charge Q , 2 Q and 3 Q are at midpoint of side AB, centre of cube and corner of cube respectively. Match the surfaces given in List-I to the c

Question

Three point charges are kept at various places of a cube. Charge $Q$ , $2 Q$ and $3 Q$ are at midpoint of side AB, centre of cube and corner of cube respectively. Match the surfaces given in List-I to the corresponding flux passing through them given in List-II.

List - I	List - II
(I) Total flux through cube	(P) $\frac{Q}{3 ϵ _{0}}$
(II) Flux through surface ABCD	(Q) $\frac{11 Q}{24 ϵ _{0}}$
(III) Flux through surface ABFE	(R) $\frac{11 Q}{12 ϵ _{0}}$
(IV) Sum of flux through BCGF and EFGH	(S) $\frac{25 Q}{24 ϵ _{0}}$
	(T) $\frac{21 Q}{8 ϵ _{0}}$

TestHub · Accepted Answer

Using Gauss's law with fractional contributions: the edge charge $Q$ sends $\frac{1}{4}$ of its flux through the cube, the centre charge $2 Q$ sends all of it, and the corner charge $3 Q$ sends $\frac{1}{8}$ : total flux $= \frac{Q}{4 ϵ _{0}} + \frac{2 Q}{ϵ _{0}} + \frac{3 Q}{8 ϵ _{0}} = \frac{21 Q}{8 ϵ _{0}}$ (I → T).

Face ABCD receives $\frac{1}{6}$ of the centre charge's flux, i.e. $\frac{Q}{3 ϵ _{0}}$ (II → P).

Summing the contributions of all three charges face by face gives flux through ABFE $= \frac{11 Q}{24 ϵ _{0}}$ (III → Q) and through BCGF + EFGH $= \frac{25 Q}{24 ϵ _{0}}$ (IV → S).

Option (C).

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