d
Let \({\phi _A},{\phi _B}\) and \({\phi _C}\) are the electric flux linked with \(A,B\) and \(C.\)

According to gauss theorem,

\({\phi _A} + {\phi _B} + {\phi _C} = \frac{q}{{{\varepsilon _0}}}\)

\(\sin ce\,{\phi _A} = {\phi _C},\)

\(\therefore \,2{\phi _A} + {\phi _B} = \frac{q}{{{\varepsilon _0}}}\,\,\,or\,\,2{\phi _A} = \frac{q}{{{\varepsilon _0}}} - {\phi _B}\)

or,  \(2{\phi _A} = \frac{q}{{{\varepsilon _0}}} - \phi \)

(Given \({\phi _B} = \phi \)).

\(\therefore {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\phi _A} = \frac{1}{2}\left( {\frac{q}{{{\varepsilon _0}}} - \phi } \right).\)