Ten charges are placed on the circumference of a circle of radius R with constant angular separation between successive charges. Alternate charges 1,3, 5,7,9 have charge (+q) each, while 2,4,6,8,10 have charge (-q) each. The potential V and the electric field E at the centre of the circle are respectively. (Take V = 0 at infinity)

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$V = \frac{10 q}{4 π \in_{0} R}; E = \frac{10 q}{4 π \in_{0} R^{2}}$

$V = 0; E = 0$

$V = \frac{10 q}{4 π \in_{0} R}; E = 0$

$V = 0; E = \frac{10 q}{4 π \in_{0} R^{2}}$

answer is B.

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Detailed Solution

Potential at point C
$P o t e n t i a l i s s c a l a r q u a n t i t y . V_{c} = 5 \frac{k q}{r} + 5 \frac{k (- q)}{r} = 0$
Electric field at C
$F i e l d i s v e c t o r q u a n t i t y . {\vec{E}}_{C} = (\vec{E} d u e t o + q s) + (\vec{E} d u e t o - q s) = 0 + 0 [f r o m s y m m e t r y]$

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