What Is the Electric Field of a Dipole?
A dipole is a separation of opposite electrical charges and it is quantified by an electric dipole moment. The electric dipole moment associated with two equal charges of opposite polarity separated by a distance, d is defined as the vector quantity having a magnitude equal to the product of the charge and the distance between the charges and having a direction from the negative to the positive charge along the line between the charges.
It is a useful concept in dielectrics and other applications in solid and liquid materials. These applications involve the energy of a dipole and the electric field of a dipole.
How to Calculate Electric Field of a Dipole?
Consider an electric dipole with charges +q and -q separated by a distance d.
We shall for the sake of simplicity only calculate the fields along symmetry axes, i.e. a point P along the perpendicular bisector of the dipole at a distance r from the mid-point of the dipole and a point Q along the axis of the dipole at a distance r from the mid-point of the dipole.
Along the Perpendicular Bisector (Point P)
The electric fields due to the positive and negative charges (Coulomb’s law):
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\(\begin{array}{l}E_+ = \frac{1}{4πε_0} \frac{q}{r_+^2} \end{array} \) \(\begin{array}{l} =\frac{1}{4\pi \epsilon _{0}}\frac{q}{(\sqrt{r^2+(\frac{d}{2})^2})^2}\end{array} \) \(\begin{array}{l} = \frac{1}{4\pi \epsilon _{0}}(\frac{q}{r^2 + (\frac{d}{2})^2})\end{array} \)
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Similarly,
The vertical components of the electric field cancel out as P is equidistant from both charges.
Now,
Substituting this value we get,
Dipole moment
When r >> d, we can neglect the d/2 term. Thus, we have,
The dipole moment direction is defined as pointing towards the positive charge. Thus, the direction of the electric field is opposite to the dipole moment:
\(\begin{array}{l}\overrightarrow{E} = -\frac{1}{4πε_0} \frac{\overrightarrow{p}}{r^3}\end{array} \) |
Along Axis of Dipole (Point Q)
The electric fields due to the positive and negative charges are:
\(\begin{array}{l}E_+ = \frac{1}{4π\epsilon_0} \frac{q}{r_+^2} = \frac{1}{4π\epsilon_0} \frac{q}{(r~-~\frac{d}{2})^2}E_- = \frac{1}{4π\epsilon_0} \frac{q}{r_-^2} = \frac{1}{4π\epsilon_0} \frac{q}{r~+~\frac{d}{2}^2}\end{array} \) |
Since the electric fields are along the same line but in opposing directions,
Factoring r4 from denominator:
Now if r >> d, we can neglect the (d/2r)2 term becomes very much smaller than 1. Thus, we can neglect this term. The equation becomes:
Since in this case the electric field is along the dipole moment, E+ > E–,
\(\begin{array}{l}\overrightarrow{E}= \frac{1}{4πε_0} \frac{2\overrightarrow{p}}{r^3}\end{array} \) |
Notice that in both cases the electric field tapers quickly as the inverse of the cube of the distance. Compared to a point charge which only decreases as the inverse of the square of the distance, the dipoles field decreases much faster because it contains both a positive and negative charge. If they were brought to the same point their electric fields would cancel out completely but since they have a small distance separating them, they have a feeble electric field.
Watch the video and learn about electric field due to dipole
Frequently Asked Questions – FAQs
What is an electric dipole?
What is the SI unit of the dipole moment?
Give an example of an electric dipole.
How does an atom behave as a magnetic dipole?
What is electric charge?
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