Potential Due to a Electric Dipole

The electrostatic potential due to an electric dipole at an equatorial point is

An electric dipole is formed by two charges $+q$ and $-q$ located in $xy$-plane at $(0, 2) \mathrm{mm}$ and $(0, -2) \mathrm{mm}$, respectively, as shown in the figure. The electric potential at point $P(100, 100) \mathrm{mm}$ due to the dipole is $V_0$. The charges $+q$ and $–q$ are then moved to the points $(-1, 2) \mathrm{mm}$ and $(1, -2) \mathrm{mm}$, respectively. What is the value of electric potential at $P$ due to the new dipole?

Two equal charges $q$of opposite sign separated by a distance $2a$ constitute an electric dipole of dipole moment $p$. If $P$ is a point at a distance$r$from the centre of the dipole and the line joining the centre of the dipole to this point makes an angle $\theta$ with the axis of the dipole, then the potential at $P$ is given by: ($r>>2a$) (Where $p=2qa$)

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

A charge $q$ moves from points $A\left(0,1\right)$ to $B(1,0)$ as shown in figure. If $\left|p_1\right|>\left|p_2\right|$, then work done by electric force in moving charge $q$ from $A$ to $B$, in the vicinity of two short dipoles placed at the origin with their dipole moments as shown, will be

A small dipole of dipole moment $p$ is placed at a distance $2R$ from the centre of a neutral conducting sphere of radius $R.$ The direction of dipole is towards the centre of the sphere. A tangent is drawn from the centre of dipole to the sphere which meets the sphere at point $A.$

Two identical dipoles of dipole moment $P=p_0\hat{i}\left(p_0\right.$ is a positive constant) are placed on $x-$axis at points $A(a, 0, 0)$ and $B(-a, 0, 0)$ as shown. Then pick up the correct statements:

A small charged bead can slide on a circular frictionless, insulating wire frame. A point like dipole is fixed at the centre of circle, dipole moment is $\overrightarrow{p}$, initially the bead is on the plane of symmetric of the dipole. Bead is released from rest. Ignore the effect of gravity. Select the correct options.

The electric potential at the equatorial position due to the dipole is zero.

Electric potential at the equatorial point is 

At which of the following points is the electric potential due to a dipole minimum? 

The electrostatic potential due to an electric dipole at a distance $r$ varies as :

The distance between charges $+q$ and $-q$ is $2l$ and between $+2q$ and $-2q$ is $4l$. The electrostatic potential at point $P$ at a distance $r$ from centre $O$ is $-\alpha \left[\frac{ql}{r^2}\right]\times {10}^9 \mathrm{V}$, where the value of $\alpha$ is ______. (Use $\frac{1}{4\pi {\epsilon }_0}=9\times {10}^9 \mathrm{N} {\mathrm{m}}^2 {\mathrm{C}}^{-2}$)

The electrostatic potential due to a short electric dipole at a distance $r$ varies as:

Two electric dipoles $\overrightarrow{P_1}=-4Qa\widehat{i}$ and $\overrightarrow{P_2}=-2Qa\widehat{\mathrm{i}}$ are at points $A$ and $B$ separate by distance $r.$ Find the distance from point $A$ where net electric potential is zero.

In the given dipole, for $r>>2l$ , the electric potential at $A$ will be

In given dipole, for $r>>2\mathcal{l}$, electric potential at $A$ will be

The given dipole has charges $q$ and $-q$ separated by distance $\mathcal{l}$. The potential at $A$ due to dipole (assuming $r>>\mathcal{l}$) is

An electric dipole is fixed at the origin of coordinates. Its moment is directed in the positive $\mathrm{x}$ -direction. A positive charge is moved from the point $\left(\mathrm{r},\mathrm{ }0\right)$ to the point $\left(-\mathrm{r},\mathrm{ }0\right)$ by an external agent. In this process, the work done by the agent is

A short dipole is placed along $X$-axis with centre at origin. The electric field at a point $P$, which is at a distance $r$ from origin such that, $\overrightarrow{OP}=\overrightarrow{r}$ makes an angle of $45°$ with $X$-axis, is directed along a direction making -