A point charge causes an electric flux of $- 2 \times 10^{4} {Nm}^{2} C^{- 1}$ to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is :
$(Given ϵ_{0} = 8.85 \times 10^{- 12} C^{2} N^{- 1} m^{- 2})$

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$- 17.7 \times 10^{- 8} C$

$- 15.7 \times 10^{- 8} C$

$15.7 \times 10^{- 8} C$

$17.7 \times 10^{- 8} C$

answer is A.

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Detailed Solution

$\begin{aligned} ϕ = - 2 \times 10^{4} \frac{{Nm}^{2}}{C} \\ r = 8.0 cm \\ ϕ = \frac{q}{ϵ_{0}} \Rightarrow q = ϵ_{0} ϕ \\ = (8.85 \times 10^{- 12}) \times (- 2 \times 10^{4}) \\ q = - 17.7 \times 10^{- 8} C \end{aligned}$

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