Question

Calculate the total charge enclosed by a closed surface if number of lines entering it are 10000 and leaving are 30000.

Answer 1

by gauss theorem, €=q/e°
where €is flux, q is charge, e° is absolute permittivity.
therefore q=€.e°
q=(30000-10000).8.854×10^-12 C

Answer 2

Answer: The charge enclosed in the closed body is 17.708 $\bold{\times 10^{-8} C}$  

Solution:

The given system has a closed surface with number of lines entering and leaving, so the total charge can be found from Gauss Law.

Given data suggest that, the closed surface of electric field has an area, assumed to be A.

Now given as entering lines = 10000 and leaving lines = 30000

Net flux = Leaving lines – Entering lines = 30000 – 10000 = 20000

Now we also know that Electric flux is given by total charge as –

Gauss theorem –Electric Flux = $\frac{Q_{n e t}}{\varepsilon_{0}}$

$\begin{array}{l}{\phi=\frac{Q_{n e t}}{\varepsilon_{0}}} \\ {Q_{n e t}=\varepsilon_{0} \phi=8.854 \times 10^{-12} \times 20000} \\ {Q_{n e t}=8.854 \times 10^{-12} \times 2 \times 10^{4}=17.708 \times 10^{-8}} \\ \bold{ {Q_{n e t}=17.708 \times 10^{-8} C}\end{array}}$