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

Two unlike charges of magnitude $q$ are separated by a distance $2d$. The potential at a point midway between them is

Two identical positive charges are placed on the $y$-axis at $y=-a$ and $y=+a$. The variation of $V$ (electric potential) along $x$-axis is shown by graph

Two charged spheres of radii $10\, cm$ and $15\, cm$ are connected by a thin wire. No current will flow, if they have

A charge $ + q$ is fixed at each of the points $x = {x_0},\,x = 3{x_0},\,x = 5{x_0}$..... $\infty$, on the $x - $axis and a charge $ - q$ is fixed at each of the points $x = 2{x_0},\,x = 4{x_0},x = 6{x_0}$,..... $\infty$. Here ${x_0}$ is a positive constant. Take the electric potential at a point due to a charge $Q$ at a distance $r$ from it to be $Q/(4\pi {\varepsilon _0}r)$. Then, the potential at the origin due to the above system of charges is

The charge given to a hollow sphere of radius $10\, cm$ is $3.2×10^{-19}\, coulomb$. At a distance of $4\, cm$ from its centre, the electric potential will be