In the given figure, find the distance from point $A$ where the electric field is zero (in $cm$).

Two point charges $q_{A} = 3\; \mu C$ and $q_{B} = -3\; \mu C$ are located $20\; cm$ apart in vacuum.
$(a)$ What is the electric field at the midpoint $O$ of the line $AB$ joining the two charges?
$(b)$ If a negative test charge of magnitude $1.5 \times 10^{-9}\; C$ is placed at this point,what is the force experienced by the test charge?

Two point charges $(+Q)$ and $(-2Q)$ are placed at distances $a$ and $2a$ respectively from the origin on the $X$-axis. At what distance from the origin is the electric field zero?

$A$ thin infinite sheet charge and an infinite line charge of respective charge densities $+\sigma$ and $+\lambda$ are placed parallel at $5 \ m$ distance from each other. Points $P$ and $Q$ are at $\frac{3}{\pi} \ m$ and $\frac{4}{\pi} \ m$ perpendicular distance from the line charge towards the sheet charge,respectively. $E_P$ and $E_Q$ are the magnitudes of the resultant electric field intensities at points $P$ and $Q$,respectively. If $\frac{E_P}{E_Q} = \frac{4}{a}$ for $2|\sigma| = |\lambda|$,then the value of $a$ is ...........

Four point positive charges of same magnitude $Q$ are placed at four corners of a rigid square frame in $xy$ plane as shown in the figure. The plane of the frame is perpendicular to the $z$-axis. If a negative point charge is placed at a distance $z$ away from the above frame $(z << L)$,then:

Consider a circular loop that is uniformly charged and has a radius $R = a \sqrt{2}$. Find the position along the positive $z$-axis of the Cartesian coordinate system where the electric field is maximum,assuming the ring is placed in the $xy$-plane at the origin.