Electric charge is all about us, and there are several pieces of evidence to support this claim. Have you ever rubbed a comb through a towel and brought it up to your hair? You will see that portion of your hair is drawn to the comb. This is mostly related to the production of electrical charge. We’ll try to interpret the behavior of opposing charges when held at a distance in this section. This is the Electric Dipole idea, which is an important part of electrostatics.
What is an Electric Dipole?
A pair of objects with equal and opposing charges separated by a large distance is referred to as an electric dipole. The first charge is assumed to be negative (-q), while the second charge remains positive (q). Electric dipoles in space are always directed from negative charge ‘-q’ to positive charge ‘q’ by default. The dipole’s center is the point where ‘q’ and ‘-q’ meet.
A pair of opposing charges q and -q separated by a distance d is called an Electric Dipole.
What is Electric Dipole Moment?
It’s essentially a precise measurement of the strength of an electric dipole. The dipole moment magnitude is the product of either of charges and separation distance ‘d’ between them, according to mathematical and scientific results. Keep in mind that the dipole moment is a vector measure with a negative to positive charge direction.
For a pair of equal and opposing charges, the formula for electric dipole moment is:
p = q d
- q is the magnitude of the charges,
- d is the magnitude of the distance between them, &
- p is the electric dipole moment.
The electric dipole moment is a vector quantity with a specified direction of travel from negative to positive charge.
Electric Potential due to Dipole
Assume that a dipole is formed by two charges, –q at A and +q at B, separated by a distance d. Assume that O is the midpoint of AB.
At every location P where OP = r, the electric potential corresponding to a dipole will be:
V = (1 ⁄ 4 π ε) (p cosθ ⁄ r2)
- V is the electric potential,
- p is the electric dipole moment,
- r is the distance of a point of potential, &
- θ is the angle subtended by the dipole to the point.
Case I: For θ = 0°, V = (1 ⁄ 4 π ε) (p ⁄ r2)
Case II: For θ = 90°, V = 0
Dipole Placed in an Electric Field
Despite the fact that the two forces acting on the dipole end cancel each other as free vectors, they operate as separate points. As a result, a torque is created on the dipole. Furthermore, the dipole has a spinning action as a result of the torque.
Consider an electric dipole in the presence of an electric field. The electric dipole will be subjected to some force, which is referred to as the torque. The torque is the force exerted on dipoles in an external field, and it is calculated as follows:
τ = p × E
τ = p E sinθ
- τ is the torque on dipole,
- E is the electric field, &
- θ is the angle between dipole and electric field.
As a result, a dipole tends to align itself parallel to the concerned field in the presence of a homogeneous electric field. Other requirements must also be met, such as the orientation remaining at a non-zero angle represented by the letter ‘q.’ In addition, potential energy must be stored in the dipole at a preferred orientation, ranging from q = 0 to q > 0.
Physical Significance of Dipole
The theory of an electric dipole is important not just in physics, but it is also a legitimate and important issue in chemistry.
We know that most materials are electrically neutral since they are made up of atoms and molecules. The molecules are classified into two categories based on the behavior of the pair of charges.
- Polar molecules: A polar molecule is one in which the positive charge’s center of mass does not correspond with the negative charge’s center of mass.
- Non-Polar molecules: A Non-Polar molecule is one in which the positive charge’s center of mass corresponds with the negative charge’s center of mass.
Permanent dipole moments exist in polar compounds. In the absence of an external electric field, these dipoles are arbitrarily oriented. When an electric field is applied, the polar molecules align themselves in the direction of the field.
If the net charge in a system is zero, it does not imply that there will be no electric field or that it will be missing. The electric dipole moment was used to demonstrate this. As a result, studying an electric dipole is crucial. Understanding the notion of polarisation helps us comprehend dipoles and dipole moments.
Problem 1: What is the dipole moment for a dipole having equal charges -3 C and 3 C separated with a distance of 5 cm?
Magnitude of charge, q = 3 C
Distance between the charges, d = 5 cm = 0.05 m
The formula for dipole moment is given as:
p = q d
= 3 C × 0.05 m
= 0.15 C-m
Hence, the dipole moment for given dipole is 0.15 C-m.
Problem 2: When is the torque on a dipole maximum?
The torque on a dipole in an electric field is given by,
τ = p E sinθ
When the dipole is held perpendicular to the field,i.e., θ = 90°, the torque is maximum.
Problem 3: What is the net force acting on a dipole placed in a uniform electric field?
The forces on the two charges constituting the dipole are equal and opposite.
Hence, the net force is zero.
Problem 4: An electric dipole with dipole moment 3 × 10-8 C-m is aligned at 90° with the direction of a uniform electric field of magnitude 2 × 104 N ⁄ C. Calculate the magnitude of torque acting on the dipole?
Dipole Moment, p = 3 × 10-8 C-m
Magnitude of Electric Field, E = 2 × 104 N ⁄ C
Angle between dipole and electric field, θ = 90°
The formula for torque on a dipole is given as:
τ = p E sinθ
= 3 × 10-8 C-m × 2 × 104 N ⁄ C × sin 90°
= 6 × 10-4 N-m
Hence, the magnitude of the torque acting on the dipole is 6 × 10-4 N-m.
Problem 5: What is the direction of dipole?
An electrical dipole is a pair of equal and opposite point charges q and -q, separated by a distance d.
By convention, the direction from -q (negative charge) to +q (positive charge) is said to be the direction of dipole.