Potential Due to a Point Charge

An equilateral triangle has a side length $L$. A charge $+q$ is kept at the centroid of the triangle. $P$ is a point on the perimeter of the triangle. The ratio of the minimum and maximum possible electric potentials for the point $P$ is

Derive an expression for electric potential due to point charge.

Two tiny spheres carrying charges $1.5 \mathrm{\mu C}$ and $2.5 \mathrm{\mu C}$ are located $30 \mathrm{cm}$ apart. Find the potential and electric field at the midpoint of line joining the two charges. Take, $\frac{1}{4\mathrm{\pi }{\in }_0} = 9\times {10}^9 \mathrm{N} {\mathrm{m}}^2 {\mathrm{C}}^{-2}$

A charge of $8 \mathrm{mC}$ is placed at the origin. Calculate the work done in taking a small charge of $-2\times {10}^{-9} \mathrm{C}$ from $P$ $\left(0, 0, 3 \mathrm{cm}\right)$ to a point $Q$ $\left(0, 4 \mathrm{cm}, 0\right)$ via point $R$$\left(0, 6 \mathrm{cm}, 9 \mathrm{cm}\right)$.

A spherical conducting shell of inner radius $r_1$ and outer radius $r_2$ has a charge $Q$.  A charge $q$ is placed at the center of the shell. What is the surface charge density on the inner and outer surfaces of the shell?

Two tiny spheres carrying charges $1.5 \mathrm{\mu C}$ and $2.5 \mathrm{\mu C}$ are located $30 \mathrm{cm}$ apart. Find the potential and electric field at a point $10 \mathrm{cm}$ from this midpoint in a plane normal to the line joining the two charges and passing through the midpoint.

A cube of side $b$ has a charge $q$ at each of its vertices. Determine the potential and electric field due to this charge array at the center of the cube.