Two charged identical metal spheres $A$ and $B$ repel each other with a force of $3 \times 10^{-5} \,N$. Another identical uncharged sphere $C$ is touched with sphere $A$ and then it is placed mid-way between $A$ and $B$. Then, the magnitude of net force on $C$ is

An empty thick conducting shell of inner radius $a$ and outer radius $b$ is shown in the figure. If it is observed that the inner face of the shell carries a uniform charge density $-\sigma$ and the outer surface carries a uniform charge density $\sigma'$,and a point charge $q_A$ is placed at the center of the shell,then choose the correct statement$(s)$.

Two identical point charges are placed at a separation of $l$. $P$ is a point on the line joining the charges,at a distance $x$ from any one charge. The field at $P$ is $E$. $E$ is plotted against $x$ for values of $x$ from close to zero to slightly less than $l$. Which of the following best represents the resulting curve?

Two fixed,identical conducting plates $(\alpha)$ and $(\beta)$,each of surface area $S$,are charged to $-Q$ and $q$,respectively,where $Q > q > 0$. $A$ third identical plate $(\gamma)$,free to move,is located on the other side of the plate with charge $q$ at a distance $d$ as per the figure. The third plate is released and collides with the plate $(\beta)$. Assume the collision is elastic and the time of collision is sufficient to redistribute charge amongst $(\beta)$ and $(\gamma)$.
$(a)$ Find the electric field acting on the plate $(\gamma)$ before collision.
$(b)$ Find the charges on $(\beta)$ and $(\gamma)$ after the collision.
$(c)$ Find the velocity of the plate $(\gamma)$ after the collision and at a distance $d$ from the plate $(\beta)$.

What is the angle between the strings and the tension in the strings when two spheres are suspended in a satellite as shown in the figure?

Two metal plates $(A, B)$ are kept horizontally with a separation of $(\frac{12}{\pi}) \text{ cm}$,with plate $A$ on the top. An atomizer jet sprays oil (density $1.5 \text{ g/cm}^3$) droplets of radius $1 \text{ mm}$ horizontally. All oil droplets carry a charge of $5 \text{ nC}$. The potentials $V_A$ and $V_B$ are required on plates $A$ and $B$ respectively in order to ensure the droplets do not descend. The values of $V_A$ and $V_B$ are . . . . . . . (Neglect the air resistance to the droplets and take $g = 10 \text{ m/s}^2$)