Electric Field Intensity Due to a Dipole

Electric field on the axis of a small electric dipole at a distance $r$ is $\overrightarrow{E_1}$ and $\overrightarrow{E_2}$ at a distance of $2r$ on a line of perpendicular bisector. Then

Consider two spheres of the same radius $R$ having uniformly distributed volume charge density of same magnitude but opposite sign $(+\rho$ and $-\rho ).$ The spheres overlap such that the vector joining the centres of the negative sphere to that of the positive sphere is $\overrightarrow{d}\left(d\ll R\right).$The magnitude of the electric field at a point outside the spheres at a distance $r$ in a direction making an angle $\theta$ with $\overrightarrow{d}$ is found to be $\frac{\rho }{a\left({\epsilon }_0\right)}\left(\frac{R^{3}d}{r^3}\right)\sqrt{b{\cos }^2\theta +1}.$ The value of $(a+b)$ is (Distance $r$ is measured with respect to the mid point of the line joining the centers of the two spheres.)

Electric field due to the electric dipole at the equatorial plane is given as:

The electric field at $\mathrm{X}$ due to a dipole of dipole moment $P$ is perpendicular to $\overrightarrow{\mathrm{P}}$, then the angle $\theta$ is equal to

A given charge is situated at a certain distance from an electric dipole in the axial position experiences a force $F.$ If the distance of the charge is doubled, the force acting on the charge will be : -

The magnitude of electric field intensity at point $(2, 0, 0)$ due to a dipole of dipole moment, $\overrightarrow{P}=\hat{\mathrm{i}}+\sqrt{3}\hat{\mathrm{j}}$ kept at origin is :

What is the angle between the electric dipole moment and the electric field strength due to it on the equatorial line?

Electric field of a dipole at a distance $r$ is proportional to :-

The electric field due to an electric dipole at a distance $r$ from its centre in axial position is $E$. If the dipole is rotated through an angle of $90°$ about its perpendicular axis, the electric field at the same point will be

A given charge is situated at a certain distance from an electric dipole in the end-on position experiences a force $F$. If the distance of the charge is doubled, the force acting on the charge will be :-

Two electric dipoles of moment $P$ and $64P$ are placed in opposite direction on a line at a distance of $25 \mathrm{cm}$. The electric field will be zero at point between the dipoles whose distance from the dipole of moment $P$ is :-

Electric field at a far away distance $r$ on the axis of dipole is ${\overrightarrow{E}}_0.$ What is the electric field at a distance $2r$ on perpendicular bisector?

A dipole of dipole moment $P$ is kept at the center of a ring of radius $R$ and charge $Q.$ The dipole moment has direction along the axis of the ring. The resultant force on the ring due to the dipole is:

For the same distance from centre of the dipole the ratio of electric fields at longitudinal and transverse position is 

Two point charges of $1\mathrm{ }\mathrm{\mu }\mathrm{C}$ and $-1\mathrm{ }\mathrm{\mu }\mathrm{C}$ separated by a distance of $100\mathrm{ }\mathrm{Å}$ practically form an electric dipole. Calculate the electric field at point $\mathrm{ }\mathrm{P}$ which is at a distance of $10 \mathrm{cm}$ from the midpoint and on the perpendicular bisector of the line joining the two charges.

Two charges $+ 20\mathrm{ }\text{μC}$ and $- 20 \text{μC}$ placed $10 \mathrm{mm}$ apart essentially form an electric dipole. What will be the electric field at point $P$ on the axis of the dipole which is $10 \mathrm{cm}$ away from its centre $O$ on the side of the positive charge?

For the dipole, $\mathrm{r}\mathrm{ }>>2\mathcal{l}$ is given, what would be the electric potential at A: 

Charges $-q$ and $+q$ located at $A$ and $B$ respectively with $AB=2a$ on X-axis constitute an electric dipole. $O$( origin) is the mid-point of the dipole and $P$ is a point on perpendicular bisector (Y-axis). A charge $Q$ experiences an electrostatic force $F_1$ when placed at $P$ where $\begin{array}{ll}\mathrm{OP}& =y\end{array}$ and $y>>2a.$ If $\mathrm{Q}$ is now moved along the equatorial line to ${\mathrm{P}}^{\text{'}}$ such that ${\mathrm{OP}}^{\text{'}}=\frac{\mathrm{y}}{4},\mathrm{Q}$ experiences force ${\mathrm{F}}_2.$ What is the value of $\frac{{\mathrm{F}}_1}{{\mathrm{F}}_2}?$ (consider $\frac{y}{4}>>2a$)

A dipole is placed at origin of co-ordinate system as shown in figure. What will be the electric field at point $\mathrm{P}(0, \mathrm{y})$?

For a system of two dipoles ${\overrightarrow{P}}_1$ and ${\overrightarrow{P}}_2$ as shown in the figure (both are at origin and perpendicular to each other along $x$ and $y$-axes, respectively) $(P_1$ and $P_2$) denotes magnitude of ${\overrightarrow{P}}_1$ and ${\overrightarrow{P}}_2$ is quite large in comparison to dimensions of dipoles, $\overrightarrow{E}$ is resultant electric field and $QPR$ is a quarter of circle whose centre is at $O$).