Potential due to Electric Dipole — Prelims Questions

An electric dipole consists of two point charges, $+q$ and $-q$, separated by a distance $2a$. The electric potential at a point $P$ at a distance $r$ from the center of the dipole on its axial line is $V_A$. The potential at a point $Q$ at the same distance $r$ from the center on its equatorial line is $V_E$. Assuming $r \gg a$, what is the ratio $V_A / V_E$?

An electric dipole has a dipole moment of $4 \times 10^{-9},\text{C m}$. Calculate the electric potential at a point located $0.3,\text{m}$ from the center of the dipole, on a line making an angle of $60^circ$ with the dipole axis. (Given: $1/(4\pi\epsilon_0) = 9 \times 10^9,\text{N m}^2/\text{C}^2$)

Which of the following statements is TRUE regarding the electric potential due to an electric dipole?

An electric dipole is placed along the x-axis with its center at the origin. The positive charge is at $(a, 0)$ and the negative charge is at $(-a, 0)$. At which of the following points will the electric potential be zero?

If an electric dipole of moment $\vec{p}$ is placed in a uniform electric field $\vec{E}$, the potential energy of the dipole is given by $U = -\vec{p} \cdot \vec{E}$. What is the work done in rotating the dipole from an orientation where its moment is parallel to the field to an orientation where it is perpendicular to the field?

An electric dipole of length $2a$ has charges $+q$ and $-q$. If the distance from the center of the dipole to an observation point $P$ is $r$, and $r \gg a$, how does the electric field $E$ at point $P$ vary with $r$?