Question

Charges $Q_1$ and $Q_2$ lie inside and outside respectively of a closed surface $\text{S}$. Let $E$ be the field at any point on $\text{S}$ and $\varphi$ be the flux of $E$ over $\text{S}$. Choose the correct statement (s).

• A. If $Q_1$ changes in magnitude , both $E$ and $\varphi$ will change
• B. If $Q_2$ changes in magnitude, $E$ 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)

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

According to the Gauss law flux through any closed surface is
$\varphi =\frac{q_{\text{enc}}}{{\epsilon }_0}$
Therefore flux through any surface depends only on total charge $q_{\text{enc}}$ inside the surface.

Thus, here flux through the surface $\text{S}$ will change if the charge inside it i.e, if magnitude of $Q_1$ is changes. The change in flux will not depend on the outside charge $Q_2$.

But electric field $\overrightarrow{E}$ at any point depends both on inside as well as outside charges. So, any change in magnitudes of $Q_1$ and $Q_2$ will effect the electric field around the surface.

Hence, (a), (b) and (c) are correct options.