Question

Charges $Q_1$ and $Q_2$ lie inside and outside respectively of a closed surface S. Let E be the field at any point on S and $\varphi$ be the flux of E over S

• A. If $Q_1$ changes, both E and $\varphi$ will change
• B. If $Q_2$ changes, E will change but $\varphi$ will not change
• C. If $Q_1$ =0 and $Q_2\ne 0$ then $E\ne 0$ but $\varphi =0$
• D. If $Q_1\ne 0$ and $Q_2=0$ then $E=0$ but $\varphi \ne 0$

Answer 1

Answer: (A), (B), (C)

The correct options are
A If $Q_1$ changes, both E and $\varphi$ will change
B If $Q_2$ changes, E will change but $\varphi$ will not change
C If $Q_1$ =0 and $Q_2\ne 0$ then $E\ne 0$ but $\varphi =0$

The electric field is the resultant effect due to all charges. So E will depend on both $Q_1$ and $Q_2$.

According to Gauss's law, the flux $\varphi =\frac{q_{in}}{{ϵ}_0}=\frac{Q_1}{{ϵ}_0}$. So $\varphi$ will depend only $Q_1$.

If $Q_1$ changes, E and $\varphi$ will change.

If $Q_2$ changes, E will change but $\varphi$ will not change.

If $Q_1=0,Q_2\ne 0$, $E\ne 0$ and $\varphi =0$

If $Q_1\ne 0,Q_2=0$, $E\ne 0$ and $\varphi \ne 0$