Physics - Electrostatics Question with Solution | TestHub

Step 1: Total flux through cylinder using Gauss Law By Gauss Law, total flux through the cylinder is given by: ${\varphi }_{\text{total }}=\frac{\mathrm{q}}{{\epsilon }_0}\dots (1)$ Step 2: Flux through plane surface $A$ As surfaces $\mathrm{A}\&\mathrm{C}$ is symmetrical so ${\varphi }_{\mathrm{A}}={\varphi }_{\mathrm{C}}$ ${\varphi }_{\text{total }}={\varphi }_{\mathrm{A}}+{\varphi }_{\mathrm{B}}+{\varphi }_{\mathrm{C}}=\frac{\mathrm{q}}{{\epsilon }_{\mathrm{o}}}[\text{Using Equation (1)] }$ Given Flux through curved surface ${\varphi }_B=\varphi$ So, $\begin{array}{rl}& 2{\varphi }_A+\varphi =\frac{q}{{\epsilon }_0}\\ & \Rightarrow {\varphi }_A=\frac{1}{2}\left(\frac{q}{{\epsilon }_0}-\varphi \right)\end{array}$