Electrostatics · Physics · IAT (IISER)

Consider two point charges $+q$ and $+2 q$ fixed on the $x-y$ plane at $(-\ell / 2,0)$ and $(+\ell / 2,0)$ respectively. Another point charge $-q$ having mass $m$ is released from rest at $(0,(\sqrt{3} / 2) \ell)$ on the $x y$ plane, as shown in the figure The permittivity of free space is $\epsilon_0$. What is the acceleration of the charge $-q$ at the time of release?

Particle A with charge $Q$ and particle B with charge $2 Q$ are fixed at positions $\vec{r}_A$ and $\vec{r}_B$, respectively. The force on $A$ due to $B$ is $\vec{F}_{B A}$, and that on $B$ due to $A$ is $\vec{F}_{A B}$. Which of the following options is correct?

The charge distribution inside a sphere of radius $R=2 a / b$ is given by the volume charge density $\rho=a r^2-b r^3$, where $a$ and $b$ are constants and $r$ is the radial distance from the center of the sphere. At what distance from the center of the sphere, will the electric field go to zero?