The linear charge density on upper half of a segment of ring is $\lambda$ and at lower half, it is $-\lambda$. The direction of electrical field at centre $O$ of ring is :-

Figures below show regular hexagons, with charges at the vertices. In which of the following cases the electric field at the centre is not zero

A ring of radius $R$ is charged uniformly with a charge $+\,Q$ . The electric field at a point on its axis at a distance $r$ from any point on the ring will be

Four point charges $-q, +q, +q$ and $-q$ are placed on $y$ axis at $y = -2d$, $y = -d, y = +d$ and $y = +2d$, respectively. The magnitude of the electric field $E$ at a point on the $x -$ axis at $x = D$, with $D > > d$, will vary as

A uniformly charged disc of radius $R$ having surface charge density $\sigma$ is placed in the ${xy}$ plane with its center at the origin. Find the electric field intensity along the $z$-axis at a distance $Z$ from origin :-

Charges $Q _{1}$ and $Q _{2}$ arc at points $A$ and $B$ of a right angle triangle $OAB$ (see figure). The resultant electric field at point $O$ is perpendicular to the hypotenuse, then $Q _{1} / Q _{2}$ is proportional to