Electric Dipole is Spherical Symmetric

As we already know, an electric dipole is a system of two point charges +q and -q that are opposite and equal charges separated by a small distance of 2a. The electric dipole moment is represented by a vector p of magnitude 2qa, which points in the direction of -q to +q. The electric potential at a point in an electric field is defined in terms of work done in carrying a test charge from infinity to that point in the field. Similarly, the potential difference between two points has been defined in terms of work done in carrying a test charge from one point to the other in the electric field. Since this work depends only on the location of points under consideration in the electric field, the potential and potential difference are characteristic properties of points in the electric field. This is possible only in a conservative field like an electric field. Hence, potential and the potential difference can be defined only in a conservative field.

Physical Meaning of Electric Potential:

We know that a liquid always flows from a higher level to a lower level. Heat also flows from a body at a higher temperature to a body at a lower temperature. Similarly, positive charge flows always from higher potential to lower potential. Just as the flow of liquid does not depend upon the quantity of liquid, but depends only upon the level of liquid; and the flow of heat also does not depend upon the amount of heat; similarly, the flow of positive charge does not depend upon the quantity of charge.

 Thus, the electric potential of a conductor is its electric state, which determines the direction of flow of charge when the given conductor is connected to another conductor. A positive charge always flows from a higher potential to a lower potential, while a negative charge always flows from a lower to a higher potential until the potentials become equal.

Potential Difference and Potential due to a Point Charge:

Let a test charge q0 initially position at point A, be brought in from point A to point B against the repulsive force in an electric field produced by a source charged q placed at origin O. Furthermore, let the position of point A and B concerning the source charge q placed at origin O is our rA and rB respectively. The following are important points to be remembered:

• The test charge q0 is so small that it does not disturb the original configuration, namely the charge q at the origin.

• The force applied by an external agent, to move the change q0 from A to B is just sufficient to counter the repulsive force F just to ensure that the net force acting on test charge q0 is zero and its motion is uniform.

• Since an electric field is a conservative field, therefore charge q0 may be brought in from A to B along the path or even along any other path, the work done will be the same.

Electric Dipole:

Before we go into electric potential due to an electric dipole, it is important to know what an electric dipole means. A system in which a pair of electric charges opposing charges separated by a distance d is known as an electric dipole. The electric dipole moment p is the product of any two charges multiplied by the distance between them. It moves from a negative to a positive charge. The axis of a dipole is the line that connects the two charges. Assume that the charges of an electric dipole are –q and +q, respectively and that they are separated by a modest distance of 2l. p = q x 2l  = 2ql, gives the dipole moment of such a dipole.

Potential Due to an Electric Dipole:

An electric dipole is an equal and opposite system of two point charges, placed at a small distance. Its moment, commonly known as electric dipole movement, is a vector having a magnitude equal to the product of a charge and the distance between the charges and a direction pointing from the negative to the positive charge. Let us determine electric potential due to a dipole at a point on its axial line and equatorial line:

1. Potential at a point on the axis of the dipole:

Let AB be an electric dipole formed by charges -q and +q coulomb, placed at a small distance of 2l metre apart in a vacuum. Let P be a point along the dipole axis at a distance r metre from the midpoint O of the dipole. We need to determine the electric potential at point P. The distance of P from the charge +q is (r-l) and that from the charge -q is (r+l).

 Therefore, the potential at P due to the charge +q of the dipole is:

and that due to the charge -q is:

2. Potential at a point on the equatorial line of the dipole:

An equatorial line is a line that is perpendicular to the axial line and runs through the centre of the electric dipole length. Now, suppose that point P is situated on the equatorial line of the dipole AB at a distance r metre from its midpoint OF. The potential at P due to the charge +q of the electric dipole is:

And due to the charge -q is:

Thus, electric potential due to an electric dipole is zero at every point on the equatorial line of the dipole.

Conclusion

An electric dipole is a configuration of two point charges that are equal yet opposite, separated by 2a. p, a vector quantity, which is used to represent the dipole moment. The dipole’s potential is determined by r and the angle between the position vector r and the dipole moment p. The square of r is inversely proportional to dipole potential. The dipole moment, a vector quantity, can be used to describe dipoles. The electric dipole moment in the simple electric dipole shown above points from the negative charge to the positive charge and has a magnitude equivalent to the strength of each charge multiplied by the distance between the charges.