Write the equation of electric field due to a point charge. Also name the terms in it.

An electric charge $Q$ is uniformly distributed around a semicircle of radius $a$. Calculate the electric potential at the centre of this semicircle.

An electric dipole is placed as shown in the figure.

The electric potential (in ${10}^2 \mathrm{V}$) at point $P$ due to the dipole is (${\epsilon }_0$=permittivity of free space and $\frac{1}{4\pi {\epsilon }_0}=K$)

A point $\mathrm{P}$ is $40 \mathrm{m}$ away from $20 \mathrm{\mu C}$ point charge and $20 \mathrm{m}$ from $4\mathrm{\mu C}$ point charge. The electric potential at point $\mathrm{P}$ is____$\mathrm{V}$.

($\mathrm{K}=9\times {10}^9{\mathrm{Nm}}^2{\mathrm{C}}^{-2}$)

The electric field lines of a positive charge is as shown in figure:

Give the sign of potential difference ${\mathrm{V}}_{\mathrm{p}}-{\mathrm{V}}_{\mathrm{q}}$.

The electric potential at the centre of two concentric half rings of radii $R_1$ and $R_2$, having same linear charge density $\lambda$ is

.

Eight point charges of charge $\mathrm{q}$ each are placed on the eight corners of a cube of side $\mathrm{a}$. A solid neutral metallic sphere of radius $\frac{\mathrm{a}}{3}$ is placed with its centre at the centre of the cube. As a result, charges are induced on the sphere, which form a certain pattern on its surface. The electric potential of the sphere is

A wire having a uniform linear charge density $\lambda$ is bent in the form of a ring of radius $R$. The point $A$ as shown in the figure is in the plane of the ring but not at the center. Two elements of the ring of lengths $a_1$ and $a_2$ subtend very small same angle at a point $A$. They are at distances $r_1$ and $r_2$ from the point $A$, respectively $\left(r_2>r_1\right)$