Course:
An electric dipole is located at (1, 1, 0). If the voltage at
(5, 6, 0) is 9V analyze the dipole for dipole moment in azdirection.
Electric Dipole
If two charges of equal magnitude and opposite signs are placed at a very small distance from one another, then the system is known as an electric dipole. The strength of an electric dipole is measured by its dipole moment vector. If the magnitude of the charge is and the separation between the charges is then the dipole moment is given by
The direction of the dipole moment is from the negative to the positive charge.
Let us consider two charges and be placed at a distance of . Let be the distance between the center of the dipole and the point of interest . Let and be the distance between the point P and and respectively.
Potential due to charge at P
Potential due to charge at P
The total potential at P is
Applying cosine law of vector we have
Now for a short dipole, we have
Similarly, we can see that
Therefore the potential
In the question given, the dipole is located at the position and the position of the observation point is . Therefore
Therefore
and
Let the dipole moment is given by
Therefore we have
Thus we wee that there is no component of the dipole moment in the z-direction, that is, .
Considering the dipole is kept on the x axis. Therefore
Therefore the magnitude of the dipole moment
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