Two smooth spherical non-conducting shells, each of radius $R$ and having uniformly distributed charges $Q$ and $-Q$ on their surfaces are released on a smooth non-conducting surface when the distance between their centres is $5R$. The mass of $A$ is $m$ and that of $B$ is $2m$. The speed of $A$ just before $A$ and $B$ collide is (neglect gravitational interaction, take $k=\frac{1}{4\pi {\epsilon }_0}$),

 

$AB$ and $CD$ are two large, non-parallel metallic plates connected to a battery as shown. If ${\sigma }_{\mathrm{A}}$ and ${\sigma }_{\mathrm{B}}$ be the charge densities at points $A$ and $B$, respectively, then,

A uniformly charged and infinitely long line having a linear charge density $\lambda$ is placed at a normal distance $\mathrm{y}$ from a point $\mathrm{O}$ . Consider a sphere of radius $\mathrm{R}$ with $\mathrm{O}$ as centre and $R>y$ . Electric flux through the surface of the sphere is:

The switch $S$ shown in figure is kept closed for a long time and then opened at $t=0,$ then the current in the middle $20 \mathrm{\Omega }$ resistor at $t=0.25 \mathrm{ms}$ is

There are two conducting spheres of radius $a$ and $b$ $(b>a)$ carrying equal and opposite charges. They are placed at a separation $d(>>>a\mathit{ }\mathit{\&} b).$ The capacitance of the system is

In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance $C$. The switch $S_1$ is pressed first to fully charge the capacitor $C_1$ and then released. The switch $S_2$ is then pressed to charge the capacitor $C_2$. After some time, $S_2$ is released and then $S_3$ is pressed. After some time,

In the given circuit diagram, $E=12 \mathrm{V}, C_1=4 \mathrm{\mu F}, C_2=2 \mathrm{\mu F}$, $C_3=6 \mathrm{\mu F}$ and $C_4=3 \mathrm{\mu F}$. Find the heat produced in the circuit (in $\mathrm{\mu J}$) after switch $S$ is shorted.