$A$ hollow insulated conducting sphere is given a positive charge of $10\,\mu C$. What will be the electric field at the centre of the sphere if its radius is $2\,m$?

$15$ charges, each of value $q$, are placed on the $X$-axis at an equal distance of $0.5R$. The electric flux associated with a spherical closed surface of radius $1.5R$, which has one of the charges at its center, is:

$A$ thin disc of radius $b = 2a$ has a concentric hole of radius $a$ in it (see figure). It carries uniform surface charge $\sigma$. If the electric field on its axis at height $h$ $(h << a)$ from its centre is given as $Ch$,then the value of $C$ is:

$A$ solid metallic sphere has a charge $+3 Q$. Concentric with this sphere is a conducting spherical shell having charge $-Q$. The radius of the sphere is $A$ and that of the spherical shell is $B$ $(B > A)$. The electric field at a distance $R$ $(A < R < B)$ from the centre is $(\varepsilon_0 = \text{permittivity of vacuum})$

The potential due to an electrostatic charge distribution is $V(r) = \frac{q e^{-\alpha r}}{4 \pi \varepsilon_{0} r}$,where $\alpha$ is positive. The net charge within a sphere centred at the origin and of radius $1/\alpha$ is

$A$ spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is