Sunday, September 24, 2023

# How To Find Dipole Moment Physics

## The Internal Magnetic Field Of A Dipole

Electric Dipole Moment, Force, Torque, Potential Energy, Work, Electric Field, Physics

The two types of dipole give the same prediction for the magnetic field far from the source. On the other hand, inside the source region, they give different predictions. The magnetic field between both poles is in the opposite direction to the magnetic moment , while within a current loop it is in the same direction . The restrictions of these fields must also be diverse as the sources minimize to zero sizes. This difference only matters if the dipole limit is used to analyze fields inside a magnetic material.

If a magnetic dipole is shaped by making a present loop smaller and smaller, but keeping the product of current and area even, the limiting field is

Contrasting the expressions in the previous section, this limit is exact for the internal field of the dipole.

If a magnetic dipole is formed by taking a “north pole” and a “south pole”, bring them closer and closer together but keeping the product of magnetic pole charge and distance constant, the limiting field is

## What Is Magnetic Moment

Magnetic moment, also known as magnetic dipole moment, is the measure of the objects tendency to align with a magnetic field.

Magnetic Moment is defined as magnetic strength and orientation of a magnet or other object that produces a magnetic field.

The magnetic moment is a vector quantity. The objects have a tendency to place themselves in such a way that the magnetic moment vector becomes parallel to the magnetic field lines.The direction of the magnetic moment points from the south to the north pole of a magnet. The magnetic field created by a magnet is directly proportional to the magnetic moment.

## What A Dipole Moment Is And Why It Matters

• Ph.D., Biomedical Sciences, University of Tennessee at Knoxville
• B.A., Physics and Mathematics, Hastings College

A dipole moment is a measurement of the separation of two opposite electrical charges. Dipole moments are a vector quantity. The magnitude is equal to the charge multiplied by the distance between the charges and the direction is from negative charge to positive charge:

= q · r

where is the dipole moment, q is the magnitude of the separated charge, and r is the distance between the charges.

Dipole moments are measured in the SI units of coulomb·meters , but because the charges tend to be very small in magnitude, the historical unit for a dipole moment is the Debye. One Debye is approximately 3.33 x 10-30 C·m. A typical dipole moment for a molecule is about 1 D.

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## Vector Character Of Dipole Moments

Dipole moment studies have contributed greatly to the study of the molecular structure of complex molecules, and especially so in the organic field. The following examples will illustrate some structural deductions from dipole moments.

The measured electric moments of some alkyl chlorides are given in Table 10.

TABLE 10. Dipole moments ofalkyl chlorides in the vapour state

 CH3Cl 2·14 2·15

Apart from the first member , all these simple alkyl chlorides have virtually the same dipole moment, 2·10 ± 0·05 D. The values for other homologous series are given in Table 11.

TABLE 11. Dipole moments for RX where R is any alkyl group

 X 1·66 ± 0·03 1·35 ± 0·10

It is clear that the group X introduced into these alkyl compounds imparts its own essentially constant dipole moment to the molecule. Taking the alkyl chlorides as our model, two features are involved in this constancy: firstly, the constancy of the electric moment in the bond from one alkyl chloride to another: secondly, the constancy of the geometry in its attachment to the alkyl groups.

It is of interest to consider the dipole moments produced when the above X groups are joined in pairs to form the X2 molecules.

In the use of such representation the symbol shows the direction of the vector dipole, from the positive to the negative centre.

FIG. 17.

Tim Chupp, in, 2010

## On Equatorial Line Of Electric Dipole

The formula for the equatorial line of electric dipole is:

If the dipole is short, the formula becomes:

Let O be the center of the dipole and consider point P lying on the axial line of the dipole, which is at distance r from the center O such that OP = r.

p \ is along \ and p \ is along \.

So, the electric field intensity will be:

Let it be represented by \ along with \, and the field intensity at k will be:

Let it be represented by \ parallel to \,

and perpendicular to \.

Complete the rectangle KLNM, and join \.

Now, applying the 2nd law of vector addition, \ represents the resultant electric field,

which is given by:

KN = \

\……

So, we get the electric field of a dipole in eq

Also, let LKN = \, then \KLN is:

\ …..

Now, here we will consider two cases viz: Field along the axial line of the dipole and the second one for the field along the equatorial line of the dipole.

• When Point K Lies Along the Axial Line of Dipole.At this moment, = 0° = Cos 0° = 1Now, equation becomes:

• And, \

This shows that the electric field intensity is along the axial line of the electric dipole.

• When the point K lies on the equatorial line of the dipole.At this moment, = 90° = Cos 90° = 0 From eq , we get:

• And, \

Here, the angle 90° shows that the direction of the resultant electric field intensity is perpendicular to the equatorial line, and therefore, parallel to the axial line of a dipole.

Fun Fact-

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## What Is Electric Charge

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## Define Electric Dipole Moment

Now, the dipole moment definition is given as the product of the magnitude of charges and the separation between them. The dipole moment determines the strength of an electric dipole to produce the electric field. It is denoted by P and it is a vector quantity.

Mathematically, the electric dipole moment is given by:

Consider two point charges q and -q place on dipole axis separated by a distance 2a, then the electric dipole moment is,

P = q x 2a..

Where,

q – The magnitude of the charge

2a – The separation between two charges

Equation is known as the electric dipole moment formula physics.

The direction of the dipole moment is always from the negative charge to the positive charge. The SI unit of the electric dipole moment is Coloumb-meter. The dimensional formula of an electric dipole is

ML¹T¹A¹

ML¹T¹A¹.

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## Polarity And Structure Of Molecules

Magnetic dipoles & dipole moment | Moving charges & magnetism | Physics | Khan Academy

The shape of a molecule and the polarity of its bonds determine the OVERALL POLARITY of that molecule. A molecule that contains polar bonds might not have any overall polarity, depending upon its shape. The simple definition of whether a complex molecule is polar or not depends upon whether its overall centers of positive and negative charges overlap. If these centers lie at the same point in space, then the molecule has no overall polarity . If a molecule is completely symmetric, then the dipole moment vectors on each molecule will cancel each other out, making the molecule nonpolar. A molecule can only be polar if the structure of that molecule is not symmetric.

A good example of a nonpolar molecule that contains polar bonds is carbon dioxide ). This is a linear molecule and each C=O bond is, in fact, polar. The central carbon will have a net positive charge, and the two outer oxygen atoms a net negative charge. However, since the molecule is linear, these two bond dipoles cancel each other out and the overall molecule has a zero dipole moment ).

Although a polar bond is a prerequisite for a molecule to have a dipole, not all molecules with polar bonds exhibit dipoles

For \ molecules, where \ is the central atom and \ are all the same types of atoms, there are certain molecular geometries which are symmetric. Therefore, they will have no dipole even if the bonds are polar. These geometries include linear, trigonal planar, tetrahedral, octahedral and trigonal bipyramid.

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## Calculating The Dipole Moment Of Water

Using a water molecule , it’s possible to calculate the magnitude and direction of the dipole moment. By comparing the electronegativity values of hydrogen and oxygen, there is a difference of 1.2e for each hydrogen-oxygen chemical bond. Oxygen has a higher electronegativity than hydrogen, so it exerts a stronger attraction on the electrons shared by the atoms. Also, oxygen has two lone electron pairs. So, you know the dipole moment must point toward the oxygen atoms. The dipole moment is calculated by multiplying the distance between the hydrogen and oxygen atoms by the difference in their charge. Then, the angle between the atoms is used to find the net dipole moment. The angle formed by a water molecule is known to be 104.5° and the bond moment of the O-H bond is -1.5D.

= 2cos = 1.84 D

## Introduction To Electric Dipole

An electric dipole is tagged as a pair of objects which possess equal & opposite charges, parted by a significantly small distance. Let us take two charges having equal magnitude Q, which are separated by the distance D.

Here we assume the first charge to be negative, while the second charge stays positive. You can call this particular combination as an electric dipole. Hence, we can state that an electric dipole is formed due to the grouping of equal & opposite charges when separated by an assured distance.

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## How To Calculate Electric Field Of A Dipole

Consider an electric dipole with charges +q and -q separated by a distance d.

We shall for the sake of simplicity only calculate the fields along symmetry axes, i.e. a point P along the perpendicular bisector of the dipole at a distance r from the mid-point of the dipole and a point Q along the axis of the dipole at a distance r from the mid-point of the dipole.

## The Formula Of Dipole Moment

A dipole moment is the product of the magnitude of the charge and the distance between the centres of the positive and negative charges in a system. It is denoted by the Greek letter \mu.

Mathematically,

\ = Charge \times distance of separation \)

The dipole moment is measured in Debye units. It is denoted by D. \. Here C is Coulomb and m is a meter.

The bond dipole moment arises between two atoms of different electronegativities. It can be expressed as

Here, \ is the bond dipole moment,

\ is the magnitude of the partial charges \ and d is the distance between \.

The bond dipole moment \ is also a vector quantity. The direction is parallel to the bond axis. In chemistry, the arrows that are drawn in order to symbolize dipole moments begin at the positive charge and end at the negative charge. When two atoms with varying electronegativities interact, the electrons tend to move from their initial positions to come closer to the more electronegative atom. This movement of electrons can be shown via the bond dipole moment.

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## Dipole Moment Of Bf3 And Bcl3

Boron trichloride , and boron trifluoride are the tetratomic compound having dipole moment zero, indicating that they have a regular planar structure.

From the above picture, three halogen atoms are on a plane at the corner of the equilateral triangle and a boron atom at the intersection of the medians. Therefore, the net of the BCl3 and BF3 is zero.

## Dipole Moment Of Bef2

In a beryllium fluoride molecule, the bond angle between the two beryllium-fluorine bonds is 180o. Fluorine, being the more electronegative atom, shifts the electron density towards itself. The individual bond dipole moments in a BeF2 molecule are illustrated below.

From the illustration provided above, it can be understood that the two individual bond dipole moments cancel each other out in a BeF2 molecule because they are equal in magnitude but are opposite in direction. Therefore, the net dipole moment of a BeF2 molecule is zero.

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## What Is The Dipole Moment

It is basically the exact measure of the strength associated with an electric dipole. Based on scientific and mathematical conclusions, the dipole moment magnitude is the product of either of the charges and the separation distance between them. Do remember that, the dipole moment is a vector measure whose direction runs from negative to a positive charge.

The formula for electric dipole moment for a pair of equal & opposite charges is p = qd, the magnitude of the charges multiplied by the distance between the two.

## What Is The Magnetic Dipole Moment Of A Revolving Electron

Electric dipoles & dipole moments | Electric charges & fields | Physics | Khan Academy

The magnetic dipole moment of a revolving electron is given as:

The current of an electron revolving around a heavy nucleus is given as:

The magnetic moment associated to the current of an electron revolving is given as:

Substituting the angular momentum of the revolving electron we get,

l = mVR

Therefore,

The above equation is known as Gyromagnetic ratio.

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## Potential And Field Of An Electric Dipole

An ideal dipole consists of two opposite charges with infinitesimal separation. We compute the potential and field of such an ideal dipole starting with two opposite charges at separation d > 0, and taking the limit as d 0.

Two closely spaced opposite charges ±q have a potential of the form:

Let R denote the position vector relative to the midpoint r _+\mathbf _}}} , and

Taylor expansion in expresses this potential as a series.

Rdp

The result for the dipole potential also can be expressed as:

which relates the dipole potential to that of a point charge. A key point is that the potential of the dipole falls off faster with distance R than that of the point charge.

The electric field of the dipole is the negative gradient of the potential, leading to:

Thus, although two closely spaced opposite charges are not quite an ideal electric dipole , at distances much larger than their separation, their dipole moment p appears directly in their potential and field.

As the two charges are brought closer together , the dipole term in the multipole expansion based on the ratio d/R becomes the only significant term at ever closer distances R, and in the limit of infinitesimal separation the dipole term in this expansion is all that matters. As d is made infinitesimal, however, the dipole charge must be made to increase to hold p constant. This limiting process results in a “point dipole”.

## What Is The Symbol Of Dipole Moment

The dipole moment is the calculation of the net molecular polarity at either end of the molecular dipole, which is the magnitude of the charge Q times the distance r between the charges. Dipole moment tells about charge separation in a molecule.

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## What Is An Electric Dipole

Before we start with the electric dipole moment we must understand what do we mean by the term dipole and dipole moment. An electric dipole is a pair of equal and opposite charges separated by a considerably short distance. In an electric dipole, the magnitude of both the charges will be the same, we can not consider a pair of two charges with different magnitudes.

Since an electric dipole is a pair of equal and opposite charges, therefore the total charge in an electric dipole will be zero. While studying electric dipole we should understand that the total charge of an electric dipole is zero does not mean that field of an electric dipole is zero.

## Dipoles In An External Electric Field

Consider an electric dipole placed in an external electric field. The electric dipole will experience some force and is known as the torque. The torque is the force exerted on the dipoles placed in an external electric field and is given by,

= P x E = PE Sin

Where,

E – The applied external field

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## What Is The Electric Field Of A Dipole

A dipole is a separation of opposite electrical charges and it is quantified by an electric dipole moment. The electric dipole moment associated with two equal charges of opposite polarity separated by a distance, d is defined as the vector quantity having a magnitude equal to the product of the charge and the distance between the charges and having a direction from the negative to the positive charge along the line between the charges.

It is a useful concept in dielectrics and other applications in solid and liquid materials. These applications involve the energy of a dipole and the electric field of a dipole.