A spherical conductor of radius $2 \mathrm{m}$ is charged to a potential of $120 \mathrm{V}$. It is now placed inside another hollow spherical conductor of radius $6 \mathrm{m}$. Calculate the potential of bigger sphere if the smaller sphere is made to touch the bigger sphere.

The potential difference between two points $\left(V_{\mathrm{A}}-V_{\mathrm{B}}\right)$ in an electric field $E=\left(2\hat{\mathrm{i}}-4\hat{\mathrm{j}}\right) \mathrm{N} {\mathrm{C}}^{-1}$, where $A=\left(0, 0\right)$ and $B=\left(3 \mathrm{m}, 4 \mathrm{m}\right)$, is

$P$ and $Q$ are two concentric metallic spheres. $P$ is positively charged and $Q$ is earthed. Then,

The arc $AB$ with the centre $C$ and the infinitely long wire having linear charge density $\mathrm{\lambda }$ are lying in the same plane. The minimum amount of work to be done to move a point charge $q_0$ from point $A$ to $B$ through a circular path $AB$ of radius $a$ is equal to

A charged block is projected on a rough horizontal surface with speed $v_0$. The value of coefficient of friction if the kinetic energy of the block remains constant is

Three charges $Q,+q$ and $+q$ are placed at the vertices of a right angled isosceles triangle as shown in figure. The net electrostatics energy of the configuration is zero if $Q$ is equal to

Two charges $q_1$ and $q_2$ are placed $30 \mathrm{cm}$ apart, as shown in figure. A third charge $q_3$ is moved along the arc of a circle of radius $40 \mathrm{cm}$ from $C$ to $D$. The change in the potential energy of the system is $\frac{q_3}{4{\mathrm{\pi \epsilon }}_0}k,$ where $k$ is

If linear charge density of a bent wire as shown in the figure is $\mathrm{\lambda }$. Then.