Twenty seven drops of water of the same size are equally and similarly charged. They are then united to form a bigger drop. By what factor will the electrical potential changes.........$times$

Two metal spheres $A$ and $B$ of radii $a$ and $b(a < b)$ respectively are at a large distance apart. Each sphere carries a charge of $100 \mu C$. The spheres are connected by a conducting wire, then

Two tiny spheres carrying charges $1.5 \;\mu\, C$ and $2.5\; \mu\, C$ are located $30 \;cm$ apart. Find the potential and electric field

$(a)$ at the mid-point of the line joining the two charges, and

$(b)$ at a point $10\; cm$ from this midpoint in a plane normal to the line and passing through the mid-point.

For given $\vec E = 2x\hat i + 3y\hat j$, find the potential at $(X, Y)$ if potential at origin is $5\, volts.$

$64$ identical drops each charged upto potential of $10\,mV$ are combined to form a bigger dorp. The potential of the bigger drop will be $..........\,mV$

Consider a thin spherical shell of radius $R$ with its centre at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field $|\vec{E}(r)|$ and the electric potential $V(r)$ with the distance r from the centre, is best represented by which graph?