Question

Five point charges $\frac{1}{\pi}, \frac{2}{\pi}, \frac{3}{\pi}, \frac{4}{\pi}$, and $\frac{-5}{\pi}$, nano-Coulomb are located inside a pyramid. The total electric flux through the surface of the pyramid is

• A. $180 N \cdot m ^{2} \cdot C ^{-1}$
• B. $90 N \cdot m ^{2} \cdot C ^{-1}$
• C. $55 N \cdot m^{2} \cdot C^{-1}$
• D. $5 N \cdot m ^{2} \cdot C ^{-1}$

Answer 1

Answer: (A)

According to Gauss's law, total electric flux through the surface of pyramid
$=\frac{\text { Total charge }}{\varepsilon_{0}}$
$=\frac{\Sigma q}{\varepsilon_{0}}=\frac{\left(\frac{1}{\pi}+\frac{2}{\pi}+\frac{3}{\pi}+\frac{4}{\pi}-\frac{5}{\pi}\right) \times 10^{-9}}{\varepsilon_{0}}$
$=\frac{5}{\pi \varepsilon_{0}} \times 10^{-9}=\frac{5 \times 4 \times 10^{-9}}{4 \pi \varepsilon_{0}}$
$=\frac{20 \times 10^{-9}}{4 \pi \varepsilon_{0}}$
$=20 \times 9 \times 10^{9} \times 10^{-9}$
$=180 Nm ^{2} C ^{-1}$