# What is the electric field of a dipole in spherical polar coordinates?

## What is the electric field of a dipole in spherical polar coordinates?

Fortunately, the way we’ve defined the coordinate axes gives us a nice expression for the dipole moment: →p=qaˆz, or, in spherical coordinates, →p=qa(cosθˆr−sinθˆθ). So →p. ˆr=pcosθ=qacosθ. Putting this all into the expression for the electric field gives us 14πε0r3(3pcosθˆr−→p), just as planned.

What is the dipole field at a point on axial line?

Electric field due to an electric dipole at a point on its axial line: AB is an electric dipole of two point charges −q and +q separated by small distance 2d. P is a point along the axial line of the dipole at a distance r from the midpoint O of the electric dipole.

### What is electric dipole with diagram?

An electric dipole is a pair of equal and opposite point charges -q and q, separated by a distance 2a. The direction from q to -q is said to be the direction of the dipole. where p is the electric dipole moment pointing from the negative charge to the positive charge.

What is dipole moment formula?

Dipole Moment (µ) = Charge (Q) * distance of separation (r) It is measured in Debye units denoted by ‘D’. 1 D = 3.33564 × 10-30 C.m, where C is Coulomb and m denotes a metre. The bond dipole moment that arises in a chemical bond between two atoms of different electronegativities can be expressed as follows: μ = 𝛿.d.

## How do you find the magnetic dipole moment?

The strength of that tiny magnet, the magnetic dipole moment m, is given by m = NIA, giving the units – Ampere meter square. The magnetic dipole moment is a vector quantity and its direction is given by the right-hand thumb rule.

Why dipole is from negative to positive?

showing that the dipole moment vector is directed from the negative charge to the positive charge because the position vector of a point is directed outward from the origin to that point.

### What is the relation between electric field on the axial line of a dipole and on the equatorial line of a dipole?

Explanation: The line perpendicular to the axial line and passes through the centre of the electric dipole length is called an equatorial line. Consider an electric dipole AB consisting of +q and -q charges separated by a distance 2l.

What is the relation between electric field due to a dipole at an axial and equatorial point?

The electric field at an axial point of the short dipole is →E1if the electric field at equatorial point of the same dipole is →E2, then which of the following is correct.

## What do you mean by dipole field?

A dipole field is created when two charges, with the same but opposite charges, are placed near to each other. They create charged lines that curve towards each other.

What dipole moment is polar?

Predicting molecule polarity

Formula Dipole moment
Polar AxOH 1.69
OxAy 1.85
NxAy 1.42
Nonpolar A2 0.0

### What is dipole moment electric field?

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 …

What is the relation between magnetic dipole moment and magnetic field?

The magnetic field of a magnetic dipole is proportional to its magnetic dipole moment. The dipole component of an object’s magnetic field is symmetric about the direction of its magnetic dipole moment, and decreases as the inverse cube of the distance from the object.

## How do you determine the direction of a dipole?

Answer: The direction of dipole moment is from negative to positive charge.

Can dipole moment negative?

The convention in chemistry is that the arrow representing the dipole moment goes from positive to negative. Physicist tend to use the opposite orientation. The vector points from positive to negative, on both the molecular (net) dipole moment and the individual bond dipoles.

### What is electric field due to dipole?

Two equal and opposite charges separated by some distance constitute a dipole. The electric field strength due to a dipole, far away, is always proportional to the dipole moment and inversely proportional to the cube of the distance. Dipole moment is the product of the charge and distance between the two charges.

What is the relation between the electric field on axial line electric field on equatorial line?

The line perpendicular to the axial line and passes through the centre of the electric dipole length is called an equatorial line. Consider an electric dipole AB consisting of +q and -q charges separated by a distance 2l. Let P be the point on the equatorial line at a distance r from the centre O of the dipole.

## What is the relation between electric field on axial and equatorial line?

The electric field due to a short dipole at a distance r, on the axial line, from its mid point is the same as electric field at a distance r′ on the equatorial line, from its mid point.

How do you find the electric field due to dipole?

We know that the electric field due to dipole is: On Axial Line of Electric Dipole. | E → | = | P → | 4 π ϵ 0 ⋅ 2 r ( r 2 − a 2) 2. If the dipole length is short, then 2a << r, so the formula becomes: | E → | = P → | 4 π ϵ 0 ⋅ 2 r 3. On Equatorial Line of Electric Dipole. The formula for the equatorial line of electric dipole is:

### What is the formula for equatorial line of electric dipole?

The formula for the equatorial line of electric dipole is: | E → | = | P → | 4 π ϵ 0 ⋅ 2 r (r 2 + a 2) 2 If the dipole is short, the formula becomes: | E → | = P → | 4 π ϵ 0 ⋅ 2 r 3

What is the coordinate independent form of an electric dipole moment?

So the spherical coordinate form of the dipole electric field now becomes: . This leads to the final expression for the coordinate independent form of the electric field of the electric dipole moment: . The net force on an electric dipole present in a uniform electric field is zero as forces act in opposite directions for oppositely signed charges.

## What are the radial and azimuthal components of a dipole dipole?

The radial component is , the polar angle component is and the azimuthal component is . The resultant electric field then due to the dipole oriented along the z-axis ( θ = 0) . This is a coordinate dependent form. i.e. its useful only where the spherical polar coordinate system is purported to be implemented.