Two point charges $+8 q$ and $-2 q$ are located at $X=0$ (origin) and $X=L$ respectively. The net electric field due to these two charges is zero at point $P$ on the $X$-axis. The location of point $P$ from the origin is:

Two identical point charges are placed at a separation of $d$. $P$ is a point on the line joining the charges, at a distance $x$ from any one charge. The field at $P$ is $E$. $E$ is plotted against $x$ for values of $x$ from close to zero to slightly less than $d$. Which of the following represents the resulting curve?

Two point charges of magnitudes $-8 \mu C$ and $+32 \mu C$ are separated by a distance of $15 \ cm$ in air. The position of the point from the $-8 \mu C$ charge at which the resultant electric field becomes zero is (in $cm$)

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

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

Three identical point charges are placed at the vertices of an isosceles right-angled triangle as shown. Which of the numbered vectors coincides in direction with the electric field at the mid-point $M$ of the hypotenuse?