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An electric dipole comprises two opposite charges separated by some distance (say d). An electric field can quantify the product of the magnitude of these charges with the distance of separation. We experience electric charges in our daily lives, such as we often rub our plastic scales on our hair, and then it attracts the bits of paper. Other examples include the attachment of dust and dirt on the screens of TV and monitors. The midpoint of the electric charges of the electric dipole will be the centre of the dipole. The direction of charges is always from negative to positive. They have equal and opposite charges acting on the dipole, due to which the net charge of the dipole becomes zero. HCl, H₂O and CH₃COOH are some of the examples that show electric dipole.
The Formula for Electric Dipole Moment
The product of the magnitude of charges with the distance of separation between them is quantified by an electric field. The formula for electric dipole moment will be as follows:
p=q.d
Where, q=magnitude of charge and
d=distance of separation.
Although, we know that forces acting on the dipole are equal and opposite and therefore cancel each other. However, they do still act as separate points. This causes the development of torque in the dipole.
The Formula of Electric Potential and Electric Potential due to Dipole
Electric potential is defined as the amount of work required for moving a unit charge from one point to the given point against any electric field. The formula for the determination of electric potential is as follows:
V= kqr
Where V= Electric potential
k= Coulomb’s constant
q= charge
r= distance of separation
Now, to calculate the relation between electric potential due to the dipole, suppose the charges of an electric dipole are -q and +q respectively. The distance of separation between them is ‘d’ and ‘O’ is the midpoint of AB.
Thus, the formula for electric potential due to Dipole at location P will be:
V = (1 ⁄ 4 π ε0) (p cosθ ⁄ r2)
Where V =electric potential,
p =electric dipole moment,
r =distance of a point of potential, &
θ =angle subtended by the dipole to the point.
Significance of Electric Dipole
The Significance of Electric Dipole with charges is as follows:
The matter composed of atoms and molecules is usually electrically neutral. The study of electric dipoles greatly helps in the understanding of polarisation and its concepts. Thus, based on the behaviour of the pair of charges, these molecules are of two categories:
Polar-Molecules: The centre of mass of both charges (positive and negative) in polar molecules does not coincide. They have permanent dipole moments and are randomly oriented in the absence of an electric field. If we apply an electric field, the polar molecules get aligned towards the direction of the electric field.
Non-Polar Molecules: In such molecules, the centre of mass of both charges does coincide with one another.
It is helpful in dielectrics and other applications in solid and liquid materials.
Solved Question on Electric Dipole
Q 1. Calculate the dipole moment of a dipole having equal charges, i.e., -4C and +4C. These two charges have a separation of 5 cm distance.
Solution: By using the formula for calculating dipole moment, we get:
p= q. d
p= 4 x 0.05
p= 0.20 c-m
Answer: The dipole moment of a dipole having equal charges, i.e., -4C and +4C separated by a 5 cm distance, is 0.20 cm.
Q 2. What will be the magnitude of torque acting on an electric dipole having a dipole moment of 6 × 10-7 C-m aligned at an angle of 90°? The direction of the uniform electric field has a magnitude of 4 × 102 N ⁄ C.
Solution: According to the question:
Dipole Moment = 6 × 10-7 C-m
The magnitude of uniform electric field (E) = 4 × 102 N ⁄ C
θ (Angle formed between the dipole and electric field)=90°
Substituting these values in the formula for torque on a dipole, we get:
τ = p E sinθ
τ = 6 × 10-7 × 4 × 102× sin 90°
τ = 24 × 10-5 N-m
Answer: The magnitude of torque acting on an electric dipole will be 24 × 10-5 N-m.
Q 3. Determine the torque acting on an electric dipole having a magnitude of 0.5 C-m. This dipole is placed parallel to an electric field with an intensity of 30 N/C.
Solution: According to the data available in the question:
Electric field= 30 N⁄C
θ = 0°
Electric dipole moment= 0.5 C m
Substituting these values in the formula of torque acting on a dipole, we get:
τ = p E sinθ
= p E sin0°
= 0
Answer: The torque acting on an electric dipole having a magnitude of 0.5 C-m parallel to an electric field will be 0.
Conclusion
To be quantified by an electric dipole moment, we need to calculate the product of the magnitude of charge and the distance of separation of these charges. The centre of these charges will be the centre of the dipole, and the direction of charges will always be from negative to positive charge. The formula for electric dipole moment will be p=q.d. The study of electric dipoles greatly helps understand polarisation and its concepts.
