Three charges $Q,( + q)$ and $( + q)$ are placed at the vertices of an equilateral triangle of side l as shown in the figure. If the net electrostatic energy of the system is zero, then $Q$ is equal to

The electrostatic potential $V$ at a point on the circumference of a thin non-conducting disk of radius $r$ and uniform charge density $\sigma$ is given by equation $V = 4 \sigma r$. Which of the following expression correctly represents electrostatic energy stored in the electric field of a similar charged disk of radius $R$?

A pellet carrying charge of $0.5\, coulombs$ is accelerated through a potential of $2,000\, volts$. It attains a kinetic energy equal to

In the following diagram the work done in moving a point charge from point $P$ to point $A$, $B$ and $C$ is respectively as $W_A$, $W_B$ and $W_C$ , then

A disk of radius $R$ with uniform positive charge density $\sigma$ is placed on the $x y$ plane with its center at the origin. The Coulomb potential along the $z$-axis is

$V(z)=\frac{\sigma}{2 \epsilon_0}\left(\sqrt{R^2+z^2}-z\right)$

A particle of positive charge $q$ is placed initially at rest at a point on the $z$ axis with $z=z_0$ and $z_0>0$. In addition to the Coulomb force, the particle experiences a vertical force $\vec{F}=-c \hat{k}$ with $c>0$. Let $\beta=\frac{2 c \epsilon_0}{q \sigma}$. Which of the following statement($s$) is(are) correct?

$(A)$ For $\beta=\frac{1}{4}$ and $z_0=\frac{25}{7} R$, the particle reaches the origin.

$(B)$ For $\beta=\frac{1}{4}$ and $z_0=\frac{3}{7} R$, the particle reaches the origin.

$(C)$ For $\beta=\frac{1}{4}$ and $z_0=\frac{R}{\sqrt{3}}$, the particle returns back to $z=z_0$.

$(D)$ For $\beta>1$ and $z_0>0$, the particle always reaches the origin.

Four equal charges $Q$ are placed at the four corners of a square of each side is $'a'$. Work done in removing a charge $-Q$ from its centre to infinity is