Three identical charges are placed at the three corners of an equilateral triangle as shown in the figure. Which of the following statements is true for the electric field $E$ and electric potential $V$ at the center $O$?

Consider a gravity-free container as shown. The system is initially at rest and the electric potential in the region is $V = (y^3 + 2) \text{ J/C}$. A ball of charge $q = -0.5 \text{ C}$ and mass $m = 2 \text{ kg}$ is released from rest from the base $(y=0)$. It starts to move up due to the electric field and collides with the shaded top face $(y=2 \text{ m})$ as shown. If its speed just after the collision is $1.5 \text{ m/s}$ and the time for which the ball is in contact with the shaded face is $0.1 \text{ s}$, find the external force required to hold the container fixed in its position during the collision, assuming the ball exerts a constant force on the wall during the entire span of the collision. (in $\text{ N}$)

Two particles each of mass $m$ and charge $q$ are separated by distance $r_1$ and the system is left free to move at $t = 0$. At time $t$,both the particles are found to be separated by distance $r_2$. The speed of each particle is

Six point charges are placed at the vertices of a regular hexagon of side $a$ as shown. If $E$ represents the electric field and $V$ represents the electric potential at the center $O$,then:

$A$ particle of mass $m$ and charge $q$ is kept at the top of a fixed frictionless sphere. $A$ uniform horizontal electric field $E$ is switched on. The particle loses contact with the sphere when the line joining the center of the sphere and the particle makes an angle $45^{\circ}$ with the vertical. The ratio $\frac{qE}{mg}$ is:

Let $E_1(r)$,$E_2(r)$,and $E_3(r)$ be the respective electric fields at a distance $r$ from a point charge $Q$,an infinitely long wire with constant linear charge density $\lambda$,and an infinite plane with uniform surface charge density $\sigma$. If $E_1(r_0) = E_2(r_0) = E_3(r_0)$ at a given distance $r_0$,then: