- An

**electric dipole consists of two point charges of equal magnitude but of opposite sign**and separated by a small distance.

- Consider an electric

**dipole centered at origin**and placed in

**z – axis**as shown in the figure:

- The

**potential (V)**at point P is given as:

- If the distance between the charges

**(d) is very small as compared to the distance of the point P**from the origin i.e.

If

**r >> d,**

**r**

_{2}– r_{1}≅**d cosθ**

**;**

**r**

_{1}≅ r_{2}= r ; r_{1}r_{2}≅ r^{2}**Substituting**the values in the above equation, the

**potential at point P**becomes:

- Electric field intensity

**(E) is the negative gradient of Electric Potential (V).**

Hence,

- The expressions for electric potential

**(V)**and field intensity

**(E)**above are only

**valid for a dipole centered at the origin and aligned with the z-axis.**

- To determine the

**fields produced by any arbitrary location and alignment**, we first need to define a new quantity

**p**, called the

**Dipole Moment.**

**p = Q d**

- Since the distance

**d**is a vector quantity, the dipole moment

**p is also a vector quantity.**

- Dipole moment p is a

**measure of the strength of the dipole and indicates its direction.**

- Vector

**d**is a

**directed distance that extends from negative charge (- Q) to positive charge (+ Q)**. This directed distance vector

**d**thus describes the distance between the dipole charges, as well as the orientation of the charges.

Therefore

**d**= | d | a

_{d}

Where

**| d |**is the

**distance between the charges**and

**a**defines the

_{d}**orientation or direction of the dipole.**

- Say a

**dipole is aligned along z – axis**, then directed distance d is given as:

**d**= | d | a

_{z}

From the above diagram it’s clear that:

**a**

_{z}. a_{r}= cosθHence the expression can be written as:

**Q d cosθ = Q | d | a**

_{z}. a_{r}= Q d. a_{r}= p . a_{r}- Hence electric potential

**(V)**due to a electric dipole

**centered at origin and aligned with the z axis**is rewritten as:

- The above expression no doubt is

**applicable for all and any dipole moments p, but is valid for dipoles centered at origin.**

- Electric potential

**(V)**at point P with a

**position vector r due to a dipole centered at a point with position vector r**

_{1}is given as:**ALSO READ:**

**- Gauss's Law - Theory.**

**- Gauss's Law - Application To a Point charge.**

**- Gauss's Law - Application To An Infinite Line Charge.**

**- Gauss's Law - Application To An Infinite Sheet Charge.**

**- Gauss's Law - Application To a Uniformly Charged Sphere.**

**- Numericals / Solved Examples - Gauss's Law.**

**- Scalar Electric Potential / Electrostatic Potential (V).**

**- Relationship Between Electric Field Intensity (E) and Electrostatic Potential (V).**

**- Electric Potential Due To a Circular Disk.**

**- Electric Dipole.**

**- Numericals / Solved Examples - Electric Potential and Electric Dipole.**

**- Energy Density In Electrostatic Field / Work Done To Assemble Charges.**

**- Numericals / Solved Examples - Electrostatic Energy and Energy Density.**

**- Numericals / Solved Examples - Gauss's law...**

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