The electric field due to a charge at a distance of $3\, m$ from it is $500\, N/C$. The magnitude of the charge is $.......\,\mu C$ $\left[ {\frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {{10}^9}\,\frac{{N \cdot m^2}}{{C^2}}} \right]$

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

The electric field due to a point charge $2q$ at a distance $r$ is $E$. Now, if charge $q$ is uniformly distributed over a thin spherical shell of radius $R$, the electric field at a distance $\frac{r}{2}$ $(r \gg R)$ from the center of the thin spherical shell is $E'=$ . . . . . . .

The direction $(\theta)$ of the electric field $\vec{E}$ at point $P$ due to a uniformly charged finite rod is shown in the figure. Based on the geometry provided,determine the angle $\theta$.

Two point charges $Q$ and $-3 Q$ are placed at some distance apart. If the electric field due to $-3 Q$ at the location of $Q$ is $E \hat{i}$,then the electric field due to $Q$ at the location of $-3 Q$ is:

Two point charges $(+Q)$ and $(-2Q)$ are fixed on the $X$-axis at positions $x = a$ and $x = 2a$ from the origin, respectively. At what position on the axis is the resultant electric field zero?