$A$ and $B$ are two identical blocks made of a conducting material. These are placed on a horizontal frictionless table and connected by a light conducting spring of force constant $‘K’$. Unstretched length of the spring is $L_0$. Charge $Q/2$ is given to each block. Consequently, the spring stretches to an equilibrium length $L$. Value of $Q$ is
$\sqrt {4\pi {\varepsilon _0}KL} $
$L\sqrt {\frac{K}{{4\pi {\varepsilon _0}\left( {L - {L_0}} \right)}}} $
$2L\sqrt {4\pi {\varepsilon _0}K\left( {L - {L_0}} \right)} $
$4\pi {\varepsilon _0}K\left( {L - {L_0}} \right)$
A charged particle with charge $q$ and mass $m$ starts with an initial kinetic energy $K$ at the middle of a uniformly charged spherical region of total charge $Q$ and radius $R$ . $q$ and $Q$ have opposite signs. The spherically charged region is not free to move . The value of $K_0$ is such that the particle will just reach the boundary of the spherically charged region. How much time does it take for the particle to reach the boundary of the region.
Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $30^{\circ}$ with each other. When suspended in a liquid of density $0.8 \;g\, cm ^{-3}$, the angle remains the same. If density of the material of the sphere is $1.6\; g \,cm ^{-3}$, the dielectric constant of the liquid is
There are two metallic spheres of same radii but one is solid and the other is hollow, then
Two equal negative charge $-q$ are fixed at the fixed points $(0,\,a)$ and $(0,\, - a)$ on the $Y$-axis. A positive charge $Q$ is released from rest at the point $(2a,\,0)$ on the $X$-axis. The charge $Q$ will
Two identical conducting spheres $\mathrm{P}$ and $\mathrm{S}$ with charge $Q$ on each, repel each other with a force $16 \mathrm{~N}$. A third identical uncharged conducting sphere $\mathrm{R}$ is successively brought in contact with the two spheres. The new force of repulsion between $\mathrm{P}$ and $\mathrm{S}$ is :