Charges $q$,$2q$,$3q$ and $4q$ are placed at the corners $A$,$B$,$C$ and $D$ of a square as shown in the figure. The direction of the electric field at the centre $O$ of the square is along:

$A$ point charge of $0.009 \ \mu C$ is placed at the origin. Calculate the electric field intensity due to this point charge at the point $(\sqrt{2}, \sqrt{7}, 0)$.

Find out the electric field intensity at point $A(1, 0, 2)$ due to a point charge $-20\,\mu C$ situated at point $B(0, 2, 1)$.

The electric field at the centre $O$ of a semicircle of radius $a$ having a linear charge density $\lambda$ is given by:

In the given figure, find the distance from point $A$ where the electric field is zero (in $cm$).

$4 \times 10^{10}$ electrons are removed from a neutral metal sphere of diameter $20 \text{ cm}$ placed in air. The magnitude of the electric field (in $\text{N C}^{-1}$) at a distance of $20 \text{ cm}$ from its centre is: