A very small electric dipole is placed at origin with its dipole moment directed along positive x-axis. A semicircular arc of radius R is drawn in the y-z plane with its centre at the origin. The potential at any arbitrary point on this arc is:

A short electric dipole has a dipole moment of $16 imes 10^{-9} \, C \cdot m$. The electric potential due to the dipole at a point at a distance of $0.6 \, m$ from the centre of the dipole, situated on a line making an angle of $60^\circ$ with the dipole axis is: $\left( \frac{1}{4 \pi \in_0} = 9 imes 10^9 \, N \cdot m^2/C^2 \right)$

The electric field in a certain region is $\frac{A}{{{x^3}}}.$ The potential at any point $(x,\,\,y,\,\,z)$ in this region will be (potential is zero at $\infty ,\,\,A$ is a constant)

The electric potential in volts due to an electric dipole of dipole moment $2 imes 10^{-8}$ coulomb-metre at a distance of $3 \mathrm{~m}$ on a line making an angle of $60^{\circ}$ with the axis of the dipole is

Twenty seven drops of same size are charged at 230 V each. They combine to form a bigger drop. Calculate the potential of the bigger drop.

The electric potential due to a dipole at a point on its axial line varies inversely as:

A short electric dipole has a dipole moment of $16 imes {10^{ - 9}}\,{\rm{C}}\,{\rm{m}}$. The electric potential due to the dipole at a point at a distance of ${\rm{0}}{\rm{.6 m}}$ from the centre of the dipole, situated on a line making an angle of ${\rm{60}}^\circ$ with the dipole axis is: $\left( {\frac{1}{{4\,\pi { \in _0}}}\, = \,9 imes {{10}^9}\,\,{\rm{N}}\,{{\rm{m}}^{\rm{2}}}{\rm{/}}\,{{\rm{C}}^{\rm{2}}}\,} \right)\,$

Two electric dipoles each of moment $5 imes 10^{-12}$ $\mathrm{C m}$ form a symbol '+' with their axes along the co-ordinate axes. The electric potential at a point $20 \mathrm{~cm}$ away in a direction making an angle of $30^{\circ}$ with axis is

A small electric dipole is placed at origin with its axis being directed along the positive ${x}$-axis. The direction of electric field due to the dipole at a point $(1 {~m}, \sqrt 2 {~m}, 0)$ is along the:

The electric field and the potential of an electric dipole vary with distance ${r}$ as

The electric potential due to a dipole at a point on its axis at a distance 'r' is V. If the distance is increased to '2r', the potential becomes: