Five point charges \(\frac{1}{\pi}, \frac{2}{\pi}, \frac{3}{\pi}, \frac{4}{\pi}\) and \(\frac{-5}{\pi}…
Five point charges \(\frac{1}{\pi}, \frac{2}{\pi}, \frac{3}{\pi}, \frac{4}{\pi}\) and \(\frac{-5}{\pi} \mathrm{nC}\) are located inside a pyramid. The total electric flux through the surface of the pyramid is
\(180 \mathrm{Nm}^2 \mathrm{C}^{-1}\)
\(90 \mathrm{Nm}^2 \mathrm{C}^{-1}\)
\(55 \mathrm{Nm}^2 \mathrm{C}^{-1}\)
\(5 \mathrm{Nm}^2 \mathrm{C}^{-1}\)
Solution
According to Gauss's law, total electric flux
\(\text {through the surface of pyramid }=\frac{\text { Total charge }}{\varepsilon_0}\)
\(\begin{aligned}
& =\frac{\Sigma q}{\varepsilon_0}=\frac{\left(\frac{1}{\pi}+\frac{2}{\pi}+\frac{3}{\pi}+\frac{4}{\pi}-\frac{5}{\pi}\right) \times 10^{-9}}{\varepsilon_0} \\
& =\frac{5}{\pi \varepsilon_0} \times 10^{-9}=\frac{5 \times 4 \times 10^{-9}}{4 \pi \varepsilon_0}=\frac{20 \times 10^{-9}}{4 \pi \varepsilon_0} \\
& =20 \times 9 \times 10^9 \times 10^{-9}=180 \mathrm{Nm}^2 \mathrm{C}^{-1}
\end{aligned}\)