Q129 / 160 · AP EAMCET 2020 (18 Sep Shift 2) · Physics

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

  • Correct answer
    A
    \(180 \mathrm{Nm}^2 \mathrm{C}^{-1}\)
  • B
    \(90 \mathrm{Nm}^2 \mathrm{C}^{-1}\)
  • C
    \(55 \mathrm{Nm}^2 \mathrm{C}^{-1}\)
  • D
    \(5 \mathrm{Nm}^2 \mathrm{C}^{-1}\)

Solution

According to Gauss's law, total electric flux \(\text {through the surface of pyramid }=\frac{\text { Total charge }}{\varepsilon_0}\) \(\begin{aligned} & =\frac{\Sigma q}{\varepsilon_0}=\frac{\left(\frac{1}{\pi}+\frac{2}{\pi}+\frac{3}{\pi}+\frac{4}{\pi}-\frac{5}{\pi}\right) \times 10^{-9}}{\varepsilon_0} \\ & =\frac{5}{\pi \varepsilon_0} \times 10^{-9}=\frac{5 \times 4 \times 10^{-9}}{4 \pi \varepsilon_0}=\frac{20 \times 10^{-9}}{4 \pi \varepsilon_0} \\ & =20 \times 9 \times 10^9 \times 10^{-9}=180 \mathrm{Nm}^2 \mathrm{C}^{-1} \end{aligned}\)

Hence, the correct answer is option: 'A'.

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