Question:

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 $2 r$ on a line of perpendicular bisector. Then

Updated On: Aug 1, 2023

$\overrightarrow{ E }_{2}=-\frac{\overrightarrow{ E }_{1}}{8}$
$\vec{E}_{2}=-\frac{\vec{E}_{1}}{16}$
$\overrightarrow{ E }_{1}=-\frac{\overrightarrow{ E }_{2}}{8}$
$\overrightarrow{ E }_{1}=\frac{\overrightarrow{ E }_{2}}{16}$

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The Correct Option is B

Approach Solution - 1

$\quad \overrightarrow{ E }_{2}=-\frac{\overrightarrow{ E }_{1}}{16}$ For axis $E _{1}=\frac{ k x 2 p }{ r ^{2}}$ For bisector $E _{2}=-\frac{ k p }{(2 r )^{3}}=\frac{ k p }{ 8 r ^{3}} \ldots$ (2) $E _{2}=-\frac{1}{8} \times \frac{ k p }{ r ^{3}}$ $=-\frac{1}{8} \times \frac{2}{2}$ $=-\frac{1}{8 \times 2} \times E _{1}$ $E _{2}=-\frac{ E _{1}}{ 1 6 }$

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Approach Solution -2

Ans. An electric dipole is a pair of point charges +q and -q that are placed side by side and spaced apart by d. A direction in space is defined as the line that joins the two charges.

Despite the fact that it is generally accepted that the dipole's orientation is from -q to q.
The center of the dipole is defined as the halfway between -q and +q.
A pair of electric charges with opposing signs and equal magnitude that are separated by a distance constitutes the simplest type of electric dipole.
The density of aluminum sulfate is 2.672 g/cm3.
The melting point of aluminum sulfate is 770 °F, while its boiling point is 214 °C.

An electric dipole is a pair of equal and opposite charges separated by a certain distance. The center of an electric dipole is the midpoint of the line joining the two charges.

The net charge of an electric dipole is zero since it is a pair of two equal and opposite charges.
The electric field due to a dipole has some finite value because the two equal charges are separated by a certain distance.

An electric dipole having charges +q and -q separated by distance d, is shown in the figure below.

Let two charges +q and -q be separated by a distance d, the formula for the electric dipole moment for a pair of equal & opposite charges is

p = qd

Where,

p is the Electric dipole moment
q is the magnitude of the charge
d is the distance between the two charges

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Notes on electrostatic potential and capacitance

Concepts Used:

Electrostatic Potential and Capacitance

Electrostatic Potential

The potential of a point is defined as the work done per unit charge that results in bringing a charge from infinity to a certain point.

Some major things that we should know about electric potential:

They are denoted by V and are a scalar quantity.
It is measured in volts.

Capacitance

The ability of a capacitor of holding the energy in form of an electric charge is defined as capacitance. Similarly, we can also say that capacitance is the storing ability of capacitors, and the unit in which they are measured is “farads”.

The capacitor is in Series and in Parallel as defined below;

In Series

Both the Capacitors C₁ and C₂ can easily get connected in series. When the capacitors are connected in series then the total capacitance that is C_totalis less than any one of the capacitor’s capacitance.

In Parallel

Both Capacitor C₁ and C₂ are connected in parallel. When the capacitors are connected parallelly then the total capacitance that is C_total is any one of the capacitor’s capacitance.