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Four identical charges each having a charge $q$ are placed at the points $(a, 0, 0), (0, a, 0), (- a, 0, 0)$ and $(0, - a, 0)$ . Let $V_{0}$ and $E_{0}$ be the potential and the field at the origin, $V$ and $E$ be the potential and field at all points on the $z - a x i s$ , other than the origin, then

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$V_{0} \neq 0$

$E_{0} = 0$

$V \neq 0$

$E \neq 0, a l o n g z - a x i s$

answer is A, B, C, D.

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Detailed Solution

$E_{0} = 0 a n d V_{0} = \frac{1}{4 π \in_{0}} \frac{4 Q}{a} A l s o, E = \frac{1}{4 π \in_{0}} \frac{4 Q}{z^{2} + a^{2}} \frac{z}{\sqrt{z^{2} + a^{2}}} a n d V = \frac{1}{4 π \in_{0}} \frac{4 Q}{\sqrt{z^{2} + a^{2}}}$

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