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

Answer 1

Answer: (A)

According to Gauss's law, total electric flux through the surface of pyramid
$=\frac{\text{ Total charge }}{{\epsilon }_0}$
$=\frac{\Sigma q}{{\epsilon }_0}=\frac{\left(\frac{1}{\pi }+\frac{2}{\pi }+\frac{3}{\pi }+\frac{4}{\pi }-\frac{5}{\pi }\right)\times 10^{-9}}{{\epsilon }_0}$
$=\frac{5}{\pi {\epsilon }_0}\times 10^{-9}=\frac{5\times 4\times 10^{-9}}{4\pi {\epsilon }_0}$
$=\frac{20\times 10^{-9}}{4\pi {\epsilon }_0}$
$=20\times 9\times 10^9\times 10^{-9}$
$=180N{m}^2{C}^{-1}$