Electric Dipole - Effectiveness Dipole Moment

Description:

Let a dipole be kept over a uniform electric field (i.e there will be some positive and negative charges placed at the side opposite to each other.) as shown in the figure −

In this the Positive charge of the dipole is repelled by the positive charges of the electric field at the same time, will be attracted by the negative charges of the electric field. The resultant direction of force F = qE is towards negative side of the field as shown in the figure.

Similarly, the resultant direction of force F = -qE of the negative charge of the dipole move towards positive side of the field.

Hence, there are two forces acting on a single body where both the forces are equal in magnitude and parallel to each other but opposite in direction. These forces are acting at the different points with certain distance between them. So this arrangement makes a couple of force which creates a torque due to which there will be a tendency of rotation which leads a dipole start rotating.

The torque acquired on the dipole is given by τ₁(Tou ) which is equal to the product of force and distance between the charges in a dipole. This shows Effectiveness of dipole.

So for above arrangement : τ₁ = Fr  OR τ₁ = qEr (since, F = qE )

Similarly, If some more dipoles are created with different charges and different distance between the charges of dipole and place the dipoles in the same electric field. Examples are shown in figure then

The force on 2^nd dipole will be F₂ = 1/2 qE.

The force on 3^rd dipole will be F₃ = 2 qE.

Then the torque for each dipole is given by −

τ₁ = qEr

τ₂ = 1/4(qEr)

τ₃ = 4(qEr)

So, it can be seen that all the dipoles are placed in the same electric field but the torque exerted by the 3^rd dipole is much large because the force on both the charge of dipole is large and the distance between the charges of dipole is also large. So the effectiveness of dipole is greater in this dipole.

Deciding factor for effectiveness of dipole

• The effectiveness of a dipole depends on torque which in turn is the decided by force. We know that F = qE, and as E is same for all the dipoles so charge ‘q’ is the deciding factor for the effectiveness of dipole. More the charge on  dipole more will be its effectiveness.

• Effectiveness depends on the distance between the two charges. This effectiveness of dipole is DIPOLE MOMENT.

Moment created by a dipole

Dipole Moment −

The vector addition of moment due to both the charges in a dipole gives dipole moment (P).

Moment of dipole (P) = 2ql

The quantity of charge multiplied by the radius of rotation gives the moment created by  a dipole. (moment of a charge = ql)

Since, the direction of moment of both the charge is same, so addition of moment due to both the charges in a dipole gives the moment of a dipole (moment due to both the charges = 2ql) and this moment is called dipole moment. It is symbolized by P. It is a vector quantity

Since, it is a vector quantity so it has a direction. The direction of a dipole moment is from -q towards +q.