A metallic sphere is kept in between two oppositely charged plates. The most appropriate representation of the field lines is

Consider an initially neutral hollow conducting spherical shell with inner radius $r$ and outer radius $2r.$ A point charge $+Q$ is now placed inside the shell at a distance $\frac{r}{2}$ from the center. The shell is then grounded by connecting the outer surface to the earth. P is an external point at a distance $2r$ from the point charge $+Q$ on the line passing through the center and the point charge $+Q$ as shown in the figure.



The magnitude of the force on a test charge $+q$ placed at P will be

A point particle of mass $0.5 \mathrm{kg}$ is moving along the $X$ -axis under a force described by the potential energy $V$ shown below. It is projected towards the right from the origin with a speed $v$.

What is the minimum value of $v$ for which the particle will escape infinitely far away from the origin?

Let the electrostatic field, $E$ at distance, $r$ from a point charge, $q$ not be an inverse square but instead an inverse cubic, e.g. $E=k\frac{q}{r^3}\hat{r}$, here $k$ is a constant. Consider the following two statements: (I) Flux through a spherical surface enclosing the charge is, $\varphi =\frac{q_{\mathrm{enclosed}}}{{\epsilon }_0}$. (II) A charge placed inside a uniformly charged shell will experience a force. Which of the above statements are valid?