An electric field converges at the origin whose magnitude is given by the expression $E=100\mathrm{rN}/\mathrm{C}$, where $r$ is the distance measured from the origin.

A bullet of mass $m$ and charge $q$ is fired towards a solid uniformly charged sphere of radius $R$ and total charge $+q$. If it strikes the surface of sphere with speed $u$, find the minimum value of $u$ so that it can penetrate through the sphere. (Neglect all resistance forces or friction acting on bullet except electrostatic forces)

A unit positive point charge of mass $m$ is projected with a velocity v inside the tunnel as shown. The tunnel has been made inside a uniformly charged non-conducting sphere of volume charge density $\rho$. The minimum velocity with which the point charge should be projected such that it can it reach the opposite end of the tunnel, is equal to:

Three concentric conducting spherical shells have radius $r,2\mathrm{r}$ and $3\mathrm{r}$ and $Q_1,Q_2$ and $Q_3$ are final charges, respectively. Innermost and outermost shells are already earthed as shown in figure. choose the wrong statement.

$X$ and $Y$ are large, parallel conducting plates closed to each other. Each face has an area $A.X$ is given a charge $Q$. $Y$ is without any charge. Points $A,B$and $C$ are as shown in figure:

Plates $A$ and $B$ constitutes an isolated, charge parallel plate capacitor. The inner surfaces (I and IV) of $A$ and $B$ have charges $+Q$ and $-Q$ respectively. $A$third plate $C$ with charge $+Q$ is now introduced midway between $A$ and $B$. Which of the following statements is not correct?

A positive point charge is placed at $P$ in front of an earthed metal sheet $S·Q$ and $R$ are two points between $P$ and $S$ as shown in the diagram. If the electric field strengths at $Q$ and $R$ are respectively $E_Q$ and $E_R$, which one of the following statements is/are false?