Two charges 2 nano coulombs and – 6 nano coulombs are separated by 16cm in air. The resultant electric intensity at the zero potential point which lies in between them and on the line joining them is

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1.5 NC^-1.

7500 NC^-1

15000 NC^-1

450 NC^-1

answer is A.

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Detailed Solution

$\begin{array}{l} V_{1} = V_{2} \Rightarrow \frac{q_{1}}{x} = \frac{q_{2}}{(16 - x)} \\ \frac{2 \times 10^{- 9}}{x} = \frac{6 \times 10^{- 9}}{(16 - x)} \Rightarrow x = 4 \times 10^{- 2} m \\ \Rightarrow x_{1} = 4 \times 10^{- 2} m, x_{2} = 12 \times 10^{- 2} m \\ E_{net} = E_{1} + E_{2} = \frac{1}{4 {πε}_{0}} [\frac{q_{1}}{x_{1}^{2}} + \frac{q_{2}}{x_{2}^{2}}] \\ = 9 \times 10^{9} [\frac{2 \times 10^{- 9}}{{(4 \times 10^{- 2})}^{2}} + \frac{6 \times 10^{- 9}}{{(12 \times 10^{- 2})}^{2}}] \\ E_{net} = 15, 000 {NC}^{- 1} \end{array}$