The distance between charges +q and q is and between +2q and 2q is . The electrostatic potential at point P at a distance from center O is where the value of is _______ .

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Solution

Q.
The distance between charges +q and −q is $2 λ$ and between +2q and −2q is $4 λ$ . The electrostatic potential at point P at a distance $r$ from center O is $- α [\frac{q l}{r^{2}}] \times 10^{9} V,$ where the value of $α$ is _______ . (Use $\frac{1}{4 π ε_{0}} = 9 \times 10^{9} {Nm}^{2} C^{- 2}$ ) [2024]

Ans.
(27)

$V = \frac{K {\vec{P}}_{net} \cdot \vec{r}}{r^{3}} = \frac{9 \times 10^{9} (6 q ℓ)}{r^{2}} \cos (120 °)$

$= - (27) (\frac{q ℓ}{r^{2}}) \times 10^{9} {Nm}^{2} C^{- 2}$

$\Rightarrow α = 27$

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