The charge per unit length of the four quadrants of the ring are $2\lambda$,$-2\lambda$,$\lambda$,and $-\lambda$ respectively. The electric field at the centre is

Two equal negative charges $-q$ each are fixed at the points $(0, a)$ and $(0, -a)$ on the $Y$-axis. $A$ positive charge $Q$ is released from rest at the point $(2a, 0)$ on the $X$-axis. The charge $Q$ will :-

Two electric charges $+2 \mu C$ and $-4 \mu C$ are separated by a distance $3 \ m$ in air. At a point $P$ located on the line joining the two charges and in between them, the electric potential is zero. Then the electric field at point $P$ (in $NC^{-1}$) is (in $,000$)

Under the influence of the Coulomb field of charge $+Q$,a charge $-q$ is moving around it in an elliptical orbit. Find out the correct statement$(s)$.

$A$ point charge $q$ moves from point $P$ to $S$ along the path $PQRS$ in a uniform electric field $E$ directed parallel to the positive $X$-axis. The coordinates of points $P, Q, R,$ and $S$ are $(a, b, 0), (2a, 0, 0), (a, -b, 0),$ and $(0, 0, 0)$ respectively. Calculate the work done by the electric field in this process.

The repulsive force between two point charges is $F$ when they are separated by a distance of $1 \, m$. Now,these point charges are replaced by spheres of radius $25 \, cm$ having the same charges. The distance between their centers is $1 \, m$. The repulsive force in the two cases will decrease according to: