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

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

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

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 square frame $\mathrm{ABCD}$is made of insulated wires and there is a short dipole, with dipole moment $p$, fixed in the plane of the figure. The dipole is lying at the centre of the square, making an angle $\theta$, as shown in the figure. If four point charges are placed at the four corners of the square, then the magnitude of force exerted by the dipole on the system of charges is

An electric dipole of length $20 \mathrm{c}\mathrm{m}$ having $\pm 3\times {10}^{-3} \mathrm{C}$ charge placed at ${60}^{\mathrm{o}}$ with respect to a uniform electric field experiences a torque of magnitude $6 \mathrm{N}\mathrm{ }\mathrm{m}$ . The potential energy of the dipole is

The point charges of $1\mathrm{ }\mathrm{\mu }\mathrm{C}$ and $-1\mathrm{ }\mathrm{\mu }\mathrm{C}$ are separated by a distance of $100\mathrm{ }\mathrm{Å}$. A point $\mathrm{ }\mathrm{P}$ is at a distance of $10 \mathrm{cm}$ from the midpoint and on the perpendicular bisector of the line joining the two charges. The electric field at $\mathrm{P}$ will be

Two charges $+20\mathrm{ }\mathrm{\mu }\mathrm{C}$ and $-20 \mathrm{\mu }\mathrm{C}$ are placed $10 \mathrm{mm}$ apart. The electric field at point $\mathrm{P}$, on the axis of the dipole $10 \mathrm{cm}$ away from its centre $\mathrm{O}$ on the side of the positive charge is

At great distances from an electric dipole, the electric field strength due to the dipole varies with the distance as

$E_{\mathrm{a}\mathrm{x}\mathrm{i}\mathrm{a}\mathrm{l}} \mathrm{a}\mathrm{n}\mathrm{d} E_{\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{i}\mathrm{a}\mathrm{l}}$ represents electric field at a point on the axial and equatorial line of a dipole of size $a$. If points are at a distance $r$ from the centre of the dipole, for $r>>a$

A short electric dipole is oriented along $x$-direction at origin. At which of the following point the electric field have no $x$-component.

Two point charges $q$ and $-q$ are at positions $\left(0, 0, d\right)$ and $\left(0, 0,- d\right)$, respectively. What is the electric field at $\left(a, 0, 0\right)$?

Two short dipole of dipole moment $p$ are placed at two corners of a square as shown in figure. What is the ratio of magnitudes of electric field intensity at two points $O$ and $A$, i.e., $E_{\mathrm{at} O}\text{:} E_{\mathrm{at}\mathrm{ }A}?$

Charges $\mathit{+}q$ and $\mathit{–}q$ are placed at $\mathrm{A}$ and $\mathrm{B}$ respectively which are at a distance $2L$ apart. If $\mathrm{C}$ is the midpoint between $\mathrm{A}$ and $\mathrm{B}$ then work done in moving $Q$ from $\mathrm{C}$ to $\mathrm{D}$ (through semicircular path $\mathrm{C}\mathrm{R}\mathrm{D}$ ) and from $\mathrm{C}$ to $\mathrm{\infty }$ are respectively

An electric dipole is placed at the origin and is directed along the $X$ -axis. At a point $P$, far away from the dipole, the electric field is parallel to the $Y$ -axis. $OP$ makes an angle $\theta$ with the $X$ -axis, then

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

Two point charges $q$ and $-q$ are at positions $(0,\mathrm{ }0,\mathrm{ }d)$ and $\text{(0, 0, }-d\text{)}$ respectively. What is the electric field at $(a,\mathrm{ }0,\mathrm{ }0)$?

The magnitude of electric field intensity at a point $\mathrm{B}\mathrm{ }(2,\mathrm{ }0,\mathrm{ }0)$ due to a dipole of dipole moment $\overrightarrow{P}=\widehat{i}+\sqrt{3}\widehat{j}$ kept at origin is (assume that the point $\mathrm{B}$ is at a large distance from the dipole and $\frac{1}{4\pi {\epsilon }_0}$ is $k$. )

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

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