An electric dipole is a key component in the study of electrostatics. Two charges that are opposite and equal and are spaced a short distance apart, make up this straightforward arrangement.
Potential Due to an Electric Dipole
In many branches of physics, such as electric fields and molecular interactions, an understanding of how such a dipole influences the electric potential at a place in space is helpful.
What is an Electric Dipole?
An electric dipole consists of:
A positive charge (+q) and a negative charge (–q)
These two charges are separated by a small fixed distance, say 2a
The dipole moment (p) is a vector quantity and is given by:
p = q ⋅ 2a ⋅ d
Where:
q is the magnitude of each charge
2a is the distance between the charges
d is the unit vector from the negative to the positive charge
The direction of the dipole moment is always from negative to positive charge.
Electric Potential Basics
The work required to move a unit positive charge from infinity to a point in space is known as the electric potential (V) caused by a point charge.
For a single point charge q, the potential at a distance r is:
V = 1 / 4πε0 ⋅ q / r
Where ε0 is the permittivity of free space.
Electric Potential Due to a Dipole
Consider a point P that is r from the dipole’s center. Let θ be the angle formed between the dipole axis and the line that connects the dipole’s center to point P.
We want to find the net electric potential at point P due to both charges of the dipole.
The total potential at P is the algebraic sum of potentials due to +q and –q:
V = V+q + V−q
Let’s place the dipole along the x-axis for simplicity:
The +q is at position (a,0)
The –q is at position (−a,0)
Now, using approximation for points far from the dipole (i.e., r ≫ ar), the potential due to the dipole is:
V = 1 / 4πε0 ⋅ p ⋅ r^ / r2
Where:
p is the dipole moment
r is the unit vector from the dipole to point P
r is the distance from the dipole center to point P
In terms of angle θ, this becomes:
V = 1 / 4πε0 ⋅ p cos θ / r2
Important Cases
1.Axial Line (θ = 0°)
This is the line passing through both charges (dipole axis).
Vaxial = 1 / 4πε0 ⋅ p / r2
2. Equatorial Line (θ = 90°)
This is the perpendicular bisector of the dipole.
Vequatorial = 0
This happens because the potentials due to both charges cancel each other out.
Key Points to Remember
A dipole’s potential falls off as 1 / r2, which is quicker than a single charge’s potential (1 / r). Because the electric potential is a scalar number, potentials are added algebraically rather than vectorially.
• The potential is zero on the equatorial line and greatest on the axial line; the dipole moment always moves from negative to positive charge.
Applications and Importance
The potential due to a dipole is important in:
Studying the behaviour of molecules (many molecules behave like dipoles)
Designing antennas.
Explaining interactions between atoms in chemistry and biology
How electric fields influence materials.
Summary
We can better understand how electric fields work in more complex systems than just single charges because to the electric potential caused by a dipole.
The dipole is a superb illustration of how basic charge configurations can result in profound fundamental insights because of its mathematical beauty and physical importance.
A system with two equal and opposing charges (+q and
-q) at a short distance apart is called an electric dipole (2a). The dipole moment p = q ⋅ 2a, which points from the negative to the positive charge, is what defines it.
At a position that is r from a dipole’s center and at an angle θ from the dipole axis, the electric potential V is:
V = 1 / 4πε0 ⋅ p cos θ / r2
Here, p is the dipole moment, and ε0 is the permittivity of free space.
The point is equally spaced from the dipole’s two charges on the equatorial line. The potentials resulting from the positive and negative charges cancel each other out since they are identical in magnitude but opposite in sign. Therefore, there is no net potential.
Electric potential is measured in volts (V).
Dipole moment is measured in Coulomb-meter (C·m).