For given arrangement, where four charge fixed at ends of as quare as given, find value of additional charge $Q$ to be put on one of the vertices so that component of net electric field along the vertical symmetric axis is zero at every point on the vertical

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 :-

Two point charges $Q_1, Q_2$ are fixed at $x = 0$ and $x = a$. Assuming that field strength is positive in the direction coinciding with the positive direction of $x$, then, which following option will be correct ?

Equal charges $q$ are placed at the vertices $A$ and $B$ of an equilateral triangle $ABC$ of side $a$. The magnitude of electric field at the point $C$ is

Six charges, three positive and three negative of equal magnitude are to be placed at the vertices of a regular hexagon such that the electric field at $O$ is double the electric field when only one positive charge of same magnitude is placed at $R$. Which of the following arrangements of charges is possible for $P,\,Q,\,R,\,S,\,T,\,$ and $U$ respectively

A ring of charge with radius $0.5\, m$ having a $0.02\, m$ gap, carries a charge of $+1\, C$. The field at the centre is