A point charge causes an electric flux of $-2 \times 10^4 \mathrm{Nm}^2 \mathrm{C}^{-1}$ to pass through a…

A point charge causes an electric flux of $-2 \times 10^4 \mathrm{Nm}^2 \mathrm{C}^{-1}$ to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is :
(Given $\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$)
  1. $15.7 \times 10^{-8} \mathrm{C}$
  2. $17.7 \times 10^{-8} \mathrm{C}$
  3. $-15.7 \times 10^{-8} \mathrm{C}$
  4. $-17.7 \times 10^{-8} \mathrm{C}$

Solution

$\begin{aligned} & \text { Flux }(\phi)=\frac{\theta_{\text {inc }}}{\epsilon_0} \\ & \begin{aligned} \theta_{\text {inc }} & =\epsilon_0 \phi \\ \quad= & -17.7 \times 10^{-8} \mathrm{C}\end{aligned}\end{aligned}$

Asked in: JEE Main 2025 (29 Jan Shift 2)

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