$A$ thin conducting ring of radius $R$ is given a charge $+Q.$ The electric field at the centre $O$ of the ring due to the charge on the part $AKB$ of the ring is $E.$ The electric field at the centre due to the charge on the part $ACDB$ of the ring is

The electric field at the center of a semi-circle of radius $a$ and linear charge density $\lambda$ is given by:

$A$ point charge of $10\,\mu C$ is placed at the origin. At what location on the $X$-axis should a point charge of $40\,\mu C$ be placed so that the net electric field is zero at $x = 2\,cm$ on the $X$-axis?

The potential in an electric field varies as $V = (x^2 - y^2)$. The electric lines of force in the $X-Y$ plane are

$A$ negative charge $-q$ is placed at the midpoint between two fixed equal positive charges $Q$,separated by a distance $2d$. If the negative charge is given a small displacement $x$ $(x \ll d)$ perpendicular to the line joining the positive charges,how will the net force $(F)$ acting on it approximately depend on $x$?

The electric field at the centre $O$ of a semicircle of radius $a$ having a linear charge density $\lambda$ is given by: