Four point charges are placed at the vertices of a regular hexagon as shown in the figure below. What will be the net electric field at the centre?

The unit of intensity of electric field is

$A$ uniformly charged semicircular arc of radius $r$ has linear charge density $\lambda$. What is the electric field at its centre? $(\epsilon_0 = \text{permittivity of free space})$

Two point charges $-q$ and $+q/2$ are situated at the origin $(0, 0, 0)$ and at the point $(a, 0, 0)$ respectively. The point along the $X$-axis where the electric field vanishes is:

$(a)$ Consider an arbitrary electrostatic field configuration. $A$ small test charge is placed at a null point (i.e.,where $E = 0$) of the configuration. Show that the equilibrium of the test charge is necessarily unstable.
$(b)$ Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart.

Two negative charges of equal magnitude are located in the $xy$-plane as shown in the figure. The direction of the electric field at point $P$ is