Electric Dipole with Charges

Electric charges are present widely in our everyday life. For example, whenever we rub a nylon cloth against some other fabric or our skin, we can feel the static electricity formed. An object having equal and opposite charges separated by distance ‘d’ is termed an electric dipole with charges. The midpoint between these two charges (where both charges meet) is the centre of the dipole, and the direction of the dipole is always from negative to positive. 

The charges acting on an electric dipole are equal and opposite, therefore, the net charge or the total charge in the electric dipole will be zero. However, this does not mean that the field of this electric dipole will become zero too. Let us learn about the electric dipole with charges in detail. 

Electric Dipole Moment

An electric dipole is the pair of equal and opposite charges with a separation of distance ‘d’. The electric dipole moment will be the product of the magnitude of these charges with the distance of separation. Being a vector quantity, it shows the direction from negative to positive.

p = q. d

Where q = magnitude of charge and d = distance of separation.

Examples of Electric Dipole: HCl, H₂O, CH₃COOH are some of the examples that show electric dipole.

Electric Potential Due to Dipole

Suppose the charges of an electric dipole are –q and +q, respectively. The distance of separation between them is ‘d’ and ‘O’, the midpoint of which is AB i.e. along the axis of the dipole. 

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, and

θ = angle subtended by the dipole to the point.

Note: If θ = 0°, then electric potential will be equal to:

 V = (1 ⁄ 4 π ε0) (p ⁄ r2)

If θ = 90°, then the electric potential will be:

V = 0

Dipole in an Electric Field

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.

What is Torque?

The amount of force that can cause an object to rotate on its own axis is termed torque. It leads the object to acquire angular acceleration, whereas force causes it to accelerate in linear kinematics. It is a vector quantity (a quantity having both magnitude and direction), and its direction is based on the direction of force acting on it.

Torque is represented by a symbol pronounced as ‘tau’ i.e. ‘τ’.

The formula for torque is as follows:

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

As torque is a vector quantity whose direction is determined by force, the magnitude of the torque vector will be as follows:

T = F r sinθ

Here,

F – force

r – Arm length (temporary)

θ – Angle formed between the force vector and temporary arm

Solved Questions on Electric Dipole with Charges

1. Calculate the dipole moment of a dipole having equal charges i.e. -2C and +2C. These two charges have a separation of 2 cm distance.

Solution:

By using the formula for calculating dipole moment, we get:

p = q. d

p = 2 x 0.02

p = 0.04 c-m

Answer: The dipole moment of a dipole having equal charges i.e. -2C and +2C, will be 0.04 c-m.

2. Determine the magnitude of torque acting on an electric dipole having a dipole moment of 3 × 10-8 C-m aligned at an angle of 90°. The direction of the uniform electric field has a magnitude of 2 × 104 N ⁄ C.

Solution:

According to the data given in the question:

Dipole Moment = 3 × 10-8 C-m

E = 2 × 104 N ⁄ C

θ (Angle between dipole and electric field) = 90°

On applying the formula for torque on a dipole, we get:

τ = p E sinθ

τ = 3 × 10-8 × 2 × 104 × sin 90°

τ = 6 × 10-4 N-m

Answer: The magnitude of torque acting on an electric dipole with a dipole moment of 3 × 108 c-m will be 6 × 10-4 N-m.

Conclusion

An electric dipole with charges consists of equal and opposite charges separated by a distance ‘d’. The direction of this dipole is always from the negative charge to the positive charge. Both of these charges are equal and opposite, therefore, they cancel each other out, making the net charge zero. If placed in an external electric field, it causes the development of torque in the dipole. The amount of force that can cause an object to rotate about an axis is termed torque.