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 $\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$ )

<p>Given an electric flux $\phi = -2 \times 10^4 \, \text{Nm}^2\text{C}^{-1}$ through a spherical Gaussian surface with a radius of 8.0 cm (r = 0.08 m), we are to find the value of the point charge $Q$. According to Gauss's Law:</p> <p>$ \phi = \frac{Q}{\varepsilon_0} $</p> <p>Where $\varepsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2\text{N}^{-1}\text{m}^{-2}$. </p> <p>Rearranging the equation to solve for $Q$, we have:</p> <p>$ Q = \phi \varepsilon_0 $</p> <p>Substituting the given values:</p> <p>$ Q = -2 \times 10^4 \times 8.85 \times 10^{-12} $</p> <p>Calculating this yields:</p> <p>$ Q = -17.7 \times 10^{-8} \, \text{C} $</p> <p>Thus, the value of the point charge is $Q = -17.7 \times 10^{-8} \, \text{C}$.</p>