If the uniform surface charge density on an infinite plane sheet is $\sigma$,the electric field near the surface will be . . . . . . .

If an insulated non-conducting sphere of radius $R$ has a uniform charge density $\rho$,the electric field at a distance $r$ from the center of the sphere $(r < R)$ will be:

The electric field intensity at $P$ and $Q$,in the shown arrangement,are in the ratio:

The figure shows a hollow hemisphere of radius $R$ in which two charges $3q$ and $5q$ are placed symmetrically about the centre $O$ on the planar surface. The electric flux over the curved surface is

Match List-$I$ with List-$II$:

List-$I$	List-$II$
$(A)$ Electric field inside (distance $r < R$ from center) of a uniformly charged spherical shell with surface charge density $\sigma$ and radius $R$.	$(I)$ $\sigma / \varepsilon_0$
$(B)$ Electric field at distance $r$ from a uniformly charged infinite plane sheet with surface charge density $\sigma$.	$(II)$ $\sigma / 2 \varepsilon_0$
$(C)$ Electric field outside (distance $r > R$ from center) of a uniformly charged spherical shell with surface charge density $\sigma$ and radius $R$.	$(III)$ $0$
$(D)$ Electric field between $2$ oppositely charged infinite plane parallel sheets with uniform surface charge density $\sigma$.	$(IV)$ $\frac{\sigma R^2}{\varepsilon_0 r^2}$

Choose the correct answer from the options given below:

Consider a uniform spherical charge distribution of radius $R_1$ centred at the origin $O$. In this distribution,a spherical cavity of radius $R_2$,centred at $P$ with distance $OP = a = R_1 - R_2$ (see figure) is made. If the electric field inside the cavity at position $\vec{r}$ is $\vec{E}(\vec{r})$,then the correct statement$(s)$ is(are):