Four electric charges $+Q, -Q, +Q$,and $-Q$ are placed at the four corners of a square. What are the electric field $(E)$ and electric potential $(V)$ at the center of the square?

Two small spheres each carrying a charge $q$ are placed $r$ metre apart. If one of the spheres is taken around the other one in a circular path of radius $r$,the work done will be equal to

Which of the following is true for the figure showing electric lines of force? ($E$ is electrical field,$V$ is potential)

$A$ charge $Q$ is uniformly distributed over the volume of an insulating sphere of radius $R$. $A$ thin metal shell of radius $b$ $(b > R)$ with a charge $-Q$ is placed around the sphere. The space between the sphere and the shell is filled with air. Which of the following graphs correctly represents the electric field $E$ as a function of distance $r$ from the center?

Three point charges $q_1, q_2, q_3$ are placed at the vertices of a triangle. If the forces on $q_1$ and $q_2$ are $(2\hat{i} - \hat{j}) \, N$ and $(\hat{i} + 3\hat{j}) \, N$,respectively,then what will be the force on $q_3$?

$A$ disk of radius $R$ with uniform positive charge density $\sigma$ is placed on the $xy$ plane with its center at the origin. The Coulomb potential along the $z$-axis is $V(z) = \frac{\sigma}{2\epsilon_0} (\sqrt{R^2+z^2} - z)$. $A$ 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 $\beta = \frac{2c\epsilon_0}{q\sigma}$. 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.