MHTCET 22 Apr 2025 Shift 1 Paper

Concept:Gauss's law states that the net electric flux through a closed surface equals the total enclosed charge divided by the permittivity of free space, $\varepsilon_0$.Explanation:Step 1: Calculate the total charge enclosed by the Gaussian surface of radius $2\ \text{m}$.The given charges are $2\ \mu C$, $-3\ \mu C$, $4\ \mu C$, $-4\ \mu C$, and $-1\ \mu C$.$$q_{\text{enclosed}} = 2 + (-3) + 4 + (-4) + (-1)\ \mu C$$$$q_{\text{enclosed}} = (2 - 3 + 4 - 4 - 1)\ \mu C = -2\ \mu C$$Step 2: Apply Gauss's law to find the net outward flux.$$\Phi = \frac{q_{\text{enclosed}}}{\varepsilon_0} = \frac{-2\ \mu C}{\varepsilon_0}$$The negative sign indicates that the net flux is directed inward.However, the options provide only the magnitude of the flux.Therefore, taking magnitude:$$|\Phi| = \frac{2}{\varepsilon_0}\ \mu V\text{-m}$$This corresponds directly to option A.Answer:Option A: $\frac{2}{\varepsilon_0}$