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

Answer 1

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

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

E depends upon both $Q_1$ and $Q_2$ but $\varphi$ depends only on $Q_1$ because according to Gauss law flux from any surface depends only on the charge enclosed by that surface.
so if $Q_1$ changes, both E and $\varphi$ will change.
$Q_2$ changes, then E will change and $\varphi$ remains same.
$Q_1=0$, $\varphi$ is zero and E is non zero.