Question

A rod containing charge $+Q$ is brought near an initially uncharged isolated conducting rod as shown. Regions with total surface charge $+Q$ and $-Q$ are induced in the conductor as shown in the figure. The only regions where the net charge in this configuration is non-zero are indicated by the $"+"$ and $"-"$ signs. Let us denote the total flux of electric field outward through closed surface $S_1$as ${\varphi }_1$ through $S_2$ as ${\varphi }_2$, etc. Which of the following is necessarily false.

• A. ${\varphi }_1>0$
• B. ${\varphi }_2={\varphi }_1$
• C. ${\varphi }_3={\varphi }_1$
• D. ${\varphi }_4=0$

Answer 1

Answer: (B)

${\varphi }_2={\varphi }_1$

By Gauss Law, we know that $\varphi =\frac{Q_{in}}{\epsilon }$.

Therefore, clearly ${\varphi }_1>0$

${\varphi }_{1}and{\varphi }_2$ will be equal in magnitude but opposite in sign, hence, ${\varphi }_1=-{\varphi }_2$

${\varphi }_1={\varphi }_3$ since $Q_{enclosed}$ is 0.

${\varphi }_4=0$ since $Q_{enclosed}$ is 0.

Hence option 2 is incorrect.