Electric Field due to a Dipole Definition

The electric charges (positive and negative) produce fields near their surroundings. According to the electric field due to dipole definition, the field strength due to dipole is always directly proportional to the dipole moment. Moreover, it is inversely proportional to the cube of the distance of separation. As already discussed, the dipole moment is the product of the magnitude of charges with the distance of separation between these charges. Let’s study the electric field due to the dipole example and the method of calculation of it in detail.

Electric Field

The laws of Coulomb deal with the force that acts between two electric charges. This law is only applicable for a static (imbalanced) charge. The electric field is the production of motion of these charges, and it propagates through space at the speed of light. According to the Coulomb’s law:

• The electric charges will modify its surroundings by forming an electric field around it.
• If we introduce a new charge in this region, that charge will experience some force due to the electric field produced by the previous charges.

The Formula for Electric Dipole Moment

The product of the magnitude of charges with the distance of separation between them is quantified as electric dipole moment. The formula for electric dipole moment will be as follows:

p= q. d

Where q= magnitude of charge and

d= distance of separation.

Electric Field due to a Dipole

According to the electric field due to dipole definition, the field strength due to dipole is always directly proportional to the dipole moment and inversely proportional to the cube of the distance of separation. All matter is composed of atoms and atoms contain both positive and negative charges. An internal or permanent dipole moment forms if the centre of positive nuclei coincides with the centre. Therefore, it will develop some of the net dipole moment and the matter will become polarised.

Electric Field due to a Dipole (Axial Line)

E= P/2πϵo. r/ (r2−a2)2

Assume the length of the dipole is very short, therefore it becomes negligible. Thus, the formula for the electric field (on the axial line) can be written as follows:

E= P/2πϵo r3

Electric Field due to a Dipole on Equatorial Line

EA= P/4πϵo r3

Electric Field due to Dipole Examples

Electric Field due to Dipole examples includes HCl, H₂O, CH₃COOH, etc. The dipole moments of these molecules are fixed because the centre of the positive charge does not coincide with the centre of the negative charge. 

Derivation of Torque on an Electric Dipole in a Uniform Electric Field

Let us assume a dipole having +p and –q charges with a distance ‘d’ in between them placed in a uniform electric field. The strength of this field shall be ‘E’. The angle formed is the θ. 

The force on the charges will be as follows:

F+= +qE

F-= -qE

Force perpendicular to dipole:

F+= + q E sinθ

F-= – q E sinθ

As we know the formula of torque, 

Torque (τ) =Force × distance (separating the forces)

τ= dq E sinθ

The formula for dipole moment is as follows:

p= q d

τ=−pEsinθ

τ= p. E

τ= p. E= pE sinθ

Solved Question on Electric Field 

Q 1- Calculate the magnitude of an electric field at a point i.e. in the middle of two charges. These 2 point charges are 4μC and -3.2μC separated by a distance of 4cm. 

Solution:

Assume the line that joins the charges is the x-axis. Therefore, we will find the electric field due to the charge at the midpoint (d=2cm). 

The magnitude of the electric field will be as follows:

E= k q/d2

= (9×109) (4×10−6)/(0.02)2

=90× 106 N/C.

Conclusion

The electric field due to dipole definition states that the field strength due to dipole is always directly proportional to the dipole moment and is inversely proportional to the cube of the distance of separation. The laws of Coulomb deal with the force that acts between two electric charges. All matter is composed of atoms, which contain both positive and negative charges.  Electric Field due to Dipole examples includes HCl, H₂O, CH₃COOH, etc.