$A$ charge $10^{-9} \ C$ is located at the origin of a coordinate system and another charge $Q$ at $(2, 0, 0) \ m$. If the $Y$-component of the electric field at $(3, 1, 1) \ m$ is zero,calculate the value of $Q$.

Two particles $A$ and $B$ having charges $20\, \mu C$ and $-5\, \mu C$ respectively are held fixed with a separation of $5\, cm$. At what position should a third charged particle be placed so that it does not experience a net electric force?

Two non-conducting spheres of radii $R_1$ and $R_2$ and carrying uniform volume charge densities $+\rho$ and $-\rho$,respectively,are placed such that they partially overlap,as shown in the figure. At all points in the overlapping region:
$(A)$ the electrostatic field is zero
$(B)$ the electrostatic potential is constant
$(C)$ the electrostatic field is constant in magnitude
$(D)$ the electrostatic field has same direction

Four identical charges are placed at the four corners of a square. If the electric field intensity at the center of the square due to any one charge is $E$,then the resultant electric field intensity at the center of the square will be .......

The distance between two charges $25\,\mu C$ and $36\,\mu C$ is $11\,cm$. At what point on the line joining the two charges will the electric field intensity be zero?

Two charged conducting spheres of radii $5 \ cm$ and $10 \ cm$ have equal surface charge densities. If the electric field on the surface of the smaller sphere is $E$,then the electric field on the surface of the larger sphere is