$(a)\;two\;times\qquad(b)\;four\;times\qquad(c)\;be\;halved\qquad(d)\;remain\;same$

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Answer : (a) two times

Explanation :

Initial potential difference between A & B

$V_{AB}=(\large\frac{kQ}{R}-\large\frac{k2Q}{2R})-(\large\frac{kQ}{2R}-\large\frac{k2Q}{2R})$

$V_{AB}=\large\frac{kQ}{2R}$

Final potential difference between A & B

$V^{|}_{AB}=(\large\frac{2kQ}{R}-\large\frac{2kQ}{2R})-(\large\frac{2kQ}{2R}-\large\frac{2kQ}{2R})$

$V^{|}_{AB}=\large\frac{kQ}{R}$

$V^{|}_{AB} = 2 V_{AB}\;.$

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