Electric dipole- Electric Field at a point on the axis of the dipole, on the equatorial line, Practice Problems, FAQs

Have you ever thought how an electrical dipole creates an electric field around it, how the field is distributed? Is it the same everywhere? Does it vary with distance only? Or depends on the orientation of the dipole? Or both? Let’s check all the cases!

Table of content:

• Electric Field due to an Electric Dipole
• Electric Field at a point on the axis of the dipole
• Electric field at a point on the equatorial line
• Practice Problems
• FAQs

Electric Field due to an Electric Dipole:

Electric dipole can be formed with two equal but opposite charged particles separated by some distance. Electric dipole can produce an electric field around it and this field can be useful in some cases.

Electric Field at a point on the axis of the dipole:

Consider an electric dipole is placed in such a way that its midpoint is at the origin as shown in the figure. The length of the dipole is and the magnitude of the charges is . Therefore, the magnitude of the dipole moment is,

The direction of the dipole moment vector is along the line joining negative charge to positive charge.

We want to find the electric field at point M, which is distance away from the origin.

The electric field at point due to charge is,

The electric field at point due to charge is,

So, the net field is,

[]

It is clear that, along the axis of an electric dipole, the direction of the net electric field is always parallel to the direction of the electric dipole moment.

If

Therefore, the electric field due to a dipole at a long distance away along its axis is

Electric field at a point on the equatorial line:

Let, an electric dipole is placed in such a way that its midpoint is at the origin. The length of the dipole is and the magnitude of the charges is as shown in the figure. So, the magnitude of the dipole moment is, 

The direction of the dipole moment vector is along the positive x-axis (from negative charge to positive charge).

We want to find the electric field at point M on the equatorial line, which is distance away from the midpoint i.e. the origin.

The magnitude of the electric field at point M due to the charge is,

The magnitude of the electric field at point M due to the charge is,

Here,

The vertical components cancel each other. The horizontal components add up.

The negative sign indicates that the electric field vector is in the opposite direction to the dipole moment vector.

If

Practice Problems:

Question.1 There is an infinitesimally small box at a corner of the room. The electric intensity away from the box is , away from the box is . What could be inside that infinitesimally small box?

a. point charge

b. electric dipole

c. may be both

d. none of this

Answer. B electric dipole

In case of a point charge the electric intensity decreases with the square of the distance from the point charge.

In case of an electrical dipole, the electric intensity decreases with the cube of the distance from the point charge.

here, and

i.e. , so there is a dipole. 

Question.2 Two charges, each of but opposite in sign, are placed apart. What is the electric field intensity at a point at a distance of from the midpoint on the axial line of the dipole?

Answer. We know, 

Where,

Question.3 There is an infinitesimally small box at the centre. Inside the box there is a dipole. There are two concentric circles around this box of radius 1 and 2 unit respectively. The electric field at points P,Q,R,S as shown in the figure are noted as respectively.

The dipole is aligned along the line

a. A

b. B

c. C

d. D

Answer. A (electric field intensity is double along the axis as compared to on equatorial)

a.

b.

c.

d.

Answer. (c)

 Along the x axis the intensity will be (on the axis)

Along the y axis the intensity will be (on the equatorial line)

Here

So,

FAQs

Question.1 Can an electric dipole system consist of more than two point charges ?

Answer. An electrical dipole is created when there are net positive and negative charges separated by some distance. The least, an electrical dipole must contain two point charges. In case of a three or more point charge, the sum of all the positive charges should be equal in magnitude to the sum of negative charges. And the positions of the centre of charges should be separated by some distance.

Question.2 A dipole of dipole moment rests on the table. The separation between the charges is . The electric field at at a distance from the centre along the x axis is and the electric field at at a distance from the centre along the equatorial axis is . If ()

a.

b.

c.

d. none of the above

Answer. 

,

Question.3 A dipole of dipole moment rests on the table. The electric field at at a distance from the centre along the axis is and the electric field at at a distance from the centre along the equatorial axis is . If ()

a.

b.

c.

d. none of the above

Answer. none of the above (

,

Question.4 A dipole of dipole moment rests on the table. There are two opposite charges of amount are separated by distance . If the distance is doubled, what will be the dipole moment?

a.

b.

c.

d.

Answer.

Dipole moment =

as the distance is doubled, the dipole moment will also double.