The distance between charges $+\mathrm{q}$ and $-\mathrm{q}$ is $2 l$ and between $+2 \mathrm{q}$ and $-2 \mathrm{q}$ is $4 l$. The electrostatic potential at point $P$ at a distance $r$ from centre $O$ is $-\alpha\left[\frac{q l}{r^2}\right] \times 10^9 \mathrm{~V}$, where the value of $\alpha$ is____. (Use $\left.\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{Nm}^2 \mathrm{C}^{-2}\right)$
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$STATEMENT-1$ For practical purposes, the earth is used as a reference at zero potential in electrical circuits.and
$STATEMENT-2$ The electrical potential of a sphere of radius $R$ with charge $\mathrm{Q}$ uniformly distributed on the surface is given by $\frac{\mathrm{Q}}{4 \pi \varepsilon_0 R}$.
Two identical thin rings, each of radius $R $ meter are coaxially placed at distance $R$ meter apart. If $Q_1$ and $Q_2$ coulomb are respectively the charges uniformly spread on the two rings, the work done in moving a charge $q$ from the centre of one ring to that of the other is
Sixty four conducting drops each of radius $0.02 m$ and each carrying a charge of $5 \,\mu C$ are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be ............
Three charged particles having charges $q,-2 q$ and $q$ are placed in a line at points $(-a, 0),(0,0)$ and $(a, 0)$ respectively. The expression for electric potential at $P(r, 0)$ for $r \gg a$ is ...............
A parallel plate condenser with a dielectric of dielectric constant $K$ between the plates has a capacity $C$ and is charged to a potential $V\ volt$. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is
Two condensers of capacities $2C$ and $C$ are joined in parallel and charged upto potential $V$. The battery is removed and the condenser of capacity $C$ is filled completely with a medium of dielectric constant $K$. The $p.d.$ across the capacitors will now be
At distance of $5$ $cm$ and $10$ $cm $ outwards from the surface of a uniformly charged solid sphere, the potentials are $100$ $V$ and $75$ $V$ respectively . Then