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

Three concentric conducting spherical shells have radii $r, 2r$ and $3r$ and charges $q_1, q_2$ and $q_3$ respectively. Innermost and outermost shells are earthed as shown in figure. The charges shown are after earthing. Select the correct alternative.

Four charges are placed at four corners of a square as shown in the figure. The side of the square is $a$. Two charges are positive and two are negative, but their magnitudes are the same. Now the external agent starts decreasing all the sides of the square slowly and at the same rate. What happens to the electrical potential energy of the system and what will be the nature of the work done by the agent?

A uniform electric field of $100 \mathrm{V} {\mathrm{m}}^{-1}$ is directed at $60°$ with the positive $x$-axis as shown in the figure. If $\mathrm{OA}=2 \mathrm{m}$, the potential difference $V_{\mathrm{O}}-V_{\mathrm{A}}$ is,

A graph of the $\mathrm{x}$-component of the electric field as a function of $x$ in a region of space is shown in figure. The $y$ and $z$ components of the electric field are zero in this region. If the electric potential is $10 \mathrm{V}$ at the origin, then the potential at $x = 2.0 \mathrm{m}$ is 

An uncharged conductor $A$, is brought near a positively charged conductor $B$. The size of the conductor $A$ is much greater than the size of the conductor $B$. Then,

Inside a hollow conducting sphere, which is uncharged, a charge $q$ is placed at its center. Let electric field at a distance $x$ from center at point $p$ be $E$ and the potential at this point be $V$. Now, some positive charge $Q$ is given to this sphere, then

Consider two concentric metal spheres . The outer sphere is given a charge $Q>0$ , then