Two identical dipoles, each of dipole moment $p$, are placed at a distance $r$ apart with their axes perpendicular to each other. The force between the dipoles is proportional to:

Consider a circular ring of radius $r$, uniformly charged with linear charge density $\lambda$. Find the electric potential at a point on the axis at a distance $x$ from the centre of the ring. Using this expression for the potential, find the electric field at this point.

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:

Which of the following is the correct expression for the electric potential (V) at an axial point due to a dipole with dipole moment P at a distance r from its center?

Two charges each having magnitude $5 \mu \mathrm{C}$ but opposite in nature, are placed $4 \mathrm{~cm}$ apart. Find the electric field intensity of a point that is at a distance $4 \mathrm{~cm}$ from the mid-point on an axial line of the dipole.

An electric dipole with dipole moment $\mathbf{p} = p_0\mathbf{i}$ is placed at the origin. The electric potential at a point $(r, heta)$ is $V$. If $r >> a$, where $2a$ is the dipole separation, which of the following is correct regarding the equipotential surfaces?

The electric potential at a point due to a short dipole is $100 \, V$. If the distance from the dipole is doubled and the dipole moment is halved, what will be the new electric potential at that point?

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

If 7 charge $q$ are placed at corners of cube of edge length $\sqrt{3} \mathrm{~m}$ then find potential at centre of cube:

A 20 F capacitor is charged to 5 V and isolated. It is then connected in parallel with an uncharged 30 F capacitor the decrease in the energy of the system will be

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: $\left( \frac{1}{4 \pi \in_0} = 9 imes 10^9 \, N \cdot m^2/C^2 \right)$