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

The point charges $Q$ and $-2Q$ are placed at some distance apart. If the electric field at the location of $Q$ is $\vec E$  , then the electric field at the location of $-2Q$ will be :

The charge distribution along the semi-circular arc is non-uniform . Charge per unit length $\lambda $ is given as $\lambda  = {\lambda _0}\sin \theta $ , with $\theta $ measured as shown in figure. $\lambda_0$ is a positive constant. The radius of arc is $R$ . The electric field at the center $P$ of semi-circular arc is $E_1$ . The value of $\frac{{{\lambda _0}}}{{{ \in _0}{E_1}R}}$ is

What will be the magnitude of electric field at point $O$ as shown in figure ? Each side of the figure is $I$ and perpendicular to each other.

Find the electric field at point $P$ (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length $L$ carrying a charge $Q.$ The distance of the point $P$ from the centre of the rod is $a=\frac{\sqrt{3}}{2} L$.