If 2000 electric field lines enter a given volume of closed space and 4000 field lines diverge from it, then the total charge within the volume is (Given \( \varepsilon_0 = 8.85\times10^{-12}\,\mathrm{C^{2}\,m^{-2}\,N} \))
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 1.77\times10^{-8}\,\mathrm{C} \)
By Gauss's law the net electric flux out of a closed surface is \( q/\varepsilon_0 \). Taking one field line as one unit of flux, the net flux equals the number of lines going out minus the number coming in.
\( \displaystyle \Phi_{\mathrm{net}} = 4000 - 2000 = 2000\,\mathrm{N\,m^{2}\,C^{-1}} \)
\( \displaystyle q = \varepsilon_0\,\Phi_{\mathrm{net}} = 8.85\times10^{-12} \times 2000 = 1.77\times10^{-8}\,\mathrm{C} \)
The result is positive because more lines leave than enter, so the enclosed net charge is positive.