Otis Singleton
The electric dipole moment is a fundamental concept in physics and chemistry, representing the separation of positive and negative electrical charges within a system. It is a vector quantity, with a direction from the negative charge to the positive charge in physics, and the opposite in chemistry. This concept is crucial for understanding the behaviour of molecules in external electric fields, as dipoles tend to align with the field. The dipole moment is calculated using the equation p = qd, where p is the dipole moment, q is the charge, and d is the distance between the charges. The SI unit for the electric dipole moment is the coulomb-metre (C·m), while the debye (D) is used in atomic physics and chemistry. Various equations and models, such as those involving potential energy and torque, help us understand and calculate the characteristics of dipole fields.
| Characteristics | Values |
|---|---|
| Definition | A measure of the separation of positive and negative electrical charges within a system, or a measure of the system's overall polarity. |
| Formula | p = qD, where p is the dipole moment, q is the magnitude of either charge, and D is the distance between the charges. |
| SI Unit | Coulomb-metre (C⋅m) |
| Other Units | Debye (D), used in atomic physics and chemistry |
| Direction | From the negative charge to the positive charge (in physics); the convention is opposite in chemistry, where it is from positive to negative. |
| Torque | When placed in a uniform external electric field, an electric dipole experiences torque, which causes it to rotate and align with the electric field. |
| Potential Energy | The potential energy of an electric dipole in a uniform electric field is given by the formula U = −pEcos(θ), where p is the dipole moment, E is the magnitude of the electric field, and θ is the angle between the dipole moment vector and the electric field vector. |
| Experimental Work | Experiments focus on measuring the electric dipole moments (EDMs) of fundamental and composite particles, such as the electron and neutron. |
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What You'll Learn
Electric dipole moment definition
The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system. In other words, it quantifies the system's overall polarity. It is a vector quantity, with a defined direction from the negative charge to the positive charge. This convention is specific to physics, as chemistry adopts the opposite direction. The line along the direction of an electric dipole is called the axis of the dipole.
An electric dipole consists of two equal and opposite charges (+q and −q) separated by a fixed distance (d). The dipole moment is the product of the magnitude of one of the charges and the separation distance between them. The SI unit for the electric dipole moment is the coulomb-metre (C⋅m), while the debye (D) is another unit used in atomic physics and chemistry.
Theoretically, an electric dipole is defined by the first-order term of the multipole expansion, where two charges are infinitesimally close together. However, in real dipoles, there is a separation of charge. In some cases, the dimensions of an object can be disregarded, allowing it to be treated as a point particle or point charge. Two point charges, one positive and the other negative, separated by a distance, constitute an electric dipole.
The dipole moment is particularly useful when considering an overall neutral system of charges, such as a pair of opposite charges or a neutral conductor in a uniform electric field. It can be calculated from electronic structure theory, either as a response to constant electric fields or from the density matrix. Coupled cluster theory, especially CCSD(T), can provide very accurate dipole moments. Additionally, the dipole moment of a molecule can be calculated based on its molecular structure using group contribution methods.
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Electric dipole moment units
The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, or a measure of the system's overall polarity. It is a vector quantity, with a defined direction from the negative charge to the positive charge. This convention, however, is only followed in physics. In chemistry, the direction is taken to be the opposite, from positive to negative.
The SI unit for the electric dipole moment is the coulomb-metre (C⋅m). This is the standard unit used to quantify the amount of electric charge in the International System of Units (SI). The debye (D) is another unit of measurement used in atomic physics and chemistry.
The dipole moment is particularly useful when considering an overall neutral system of charges, such as a pair of opposite charges or a neutral conductor in a uniform electric field. In such a system, the relation for the electric dipole moment can be expressed as:
\[\ \\ \mathbf{p}=(+q) \mathbf{r}_{+}+(-q) \mathbf{r}_{-}=q\left(\mathbf{r}_{+}-\mathbf{r}_{-}\right)=q \mathbf{a}\]
Where \(\ \mathbf{a}\) is the vector connecting the points \(\ \mathbf{r}_{-}\) and \(\ \mathbf{r}_{+}\). This formula represents the dipole moment in terms of the charges (\(+q\), \(-q\)) and their respective positions (\(\mathbf{r}_{+}\), \(\mathbf{r}_{-}\)) within the system.
The dipole moment of a molecule can also be calculated based on its molecular structure using group contribution methods. Additionally, coupled cluster theory, especially CCSD(T), can provide very accurate dipole moments, while density functional theory can yield reasonable estimates, especially when using hybrid or double hybrid functionals.
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Dipole moment in polar molecules
The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, or the system's overall polarity. In other words, dipole moments occur when there is a separation of charge. This can occur between two ions in an ionic bond or between atoms in a covalent bond.
In polar molecules, the centres of positive and negative charges do not coincide and are separated. The polarity of a molecule is a property of the bonds between the atoms that make up the molecule. It refers to the separation of electric charge, leading to the presence of an electric dipole in the molecule. In chemistry, polarity is attributed to the difference in electronegativity of atoms in a molecule. Electronegativity refers to the magnitude of attraction that an atom has on the electrons shared in a bond. When atoms in a molecule share electrons unequally, they create a dipole moment. This occurs when one atom is more electronegative than another, resulting in that atom pulling more tightly on the shared pair of electrons.
The dipole moment is a vector quantity, and its direction is from the negative charge to the positive charge. The magnitude of the dipole moment is equal to the charge multiplied by the distance between the charges. The dipole moment of a molecule can be calculated using the equation:
> \[\ vec{mu} = sum_i q_i vec{r}_i \label{1}\]
Where \(\vec{\mu}\) is the dipole moment, \(q_i\) is the magnitude of the charge, and \(vec{r}_i\) is the distance between the charges.
The dipole moment of a molecule can also be calculated by placing the substance between charged plates. Polar molecules increase the charge stored on the plates, and the dipole moment can be obtained via the capacitance of the system.
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Calculating dipole moment in a uniform electric field
The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, or its overall polarity. It is typically calculated using the formula:
\[\mathbf{p}=(+q) \mathbf{r}_{+}+(-q) \mathbf{r}_{-}=q\left(\mathbf{r}_{+}-\mathbf{r}_{-}\right)=q \mathbf{a}\]
Where \(\mathbf{a}\) is the vector connecting the points \(\mathbf{r}_{-}\) and \(\mathbf{r}_{+}\). This formula is applicable when the net charge Q is zero, in which case the dipole moment is independent of the reference frame's origin.
In the context of a uniform electric field, the dipole moment is particularly useful for understanding the behaviour of a neutral system of charges, such as a pair of opposite charges or a neutral conductor. When placed in an external electric field, an object with an electric dipole moment experiences a torque that tends to align the dipole with the field. The potential energy of this system can be calculated using the equation:
\[U = -\mathbf{p} \cdot \mathbf{E}_{\text{ext}}\]
Where \(\mathbf{p}\) is the dipole moment and \(\mathbf{E}_{\text{ext}}\) is the external electric field. The scalar dot product indicates that the potential energy is minimised when the dipole is aligned parallel to the field and maximised when antiparallel.
Additionally, the electric field of a dipole can be calculated using the equation:
\[\mathbf{E}_{\mathrm{d}}=-\frac{1}{4 \pi \varepsilon_{0}} \nabla\left(\frac{\mathbf{r} \cdot \mathbf{p}}{r^{3}}\right)=-\frac{1}{4 \pi \varepsilon_{0}} \nabla\left(\frac{p \cos \theta}{r^{2}}\right)\]
Where \(\varepsilon_{0}\) is the electric permittivity of free space, and \(\theta\) is the angle between the dipole moment and the position vector.
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Torque on an electric dipole
An electric dipole is a pair of equal but opposite electrical charges that are separated by a distance, denoted as "d". The electric dipole moment is a measure of the separation of these positive and negative charges within the system, specifically the product of the magnitude of the charges and the distance between them. It is a vector with a direction from the negative to the positive charge.
Torque, on the other hand, is a measure of the force that causes an object to rotate around an axis. It is a vector quantity, and its magnitude is the product of the force and the distance from the point where the force is applied to the axis of rotation. Torque always works in pairs, and its direction is determined by the force acting on the axis.
When an electric dipole is placed in a uniform external electric field, the positive and negative charges experience equal magnitude forces in opposite directions. As a result, the dipole may rotate with a certain angular velocity, exhibiting transitional and rotational equilibrium.
The torque on the dipole can be calculated using the following formula:
> Torque (τ) = Force x Distance separating forces x sin(θ)
Where:
- Τ is the torque
- Force is the magnitude of the force experienced by the charges
- Distance separating forces refers to the distance between the charges, d
- Θ is the angle between the electric field and the dipole moment
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Frequently asked questions
The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, or a measure of the system's overall polarity.
An electric dipole consists of two equal but opposite charges separated by a distance. The dipole moment is represented as P = QD, where Q is the charge and D is the distance between the charges.
The SI unit for electric dipole moment is the coulomb-metre (C⋅m).
The direction of an electric dipole moment is from the negative charge to the positive charge. However, in Chemistry, the convention is taken to be the opposite, i.e. from positive to negative.
