When studying physics in the 10th grade, the topic of dipoles is considered. What does this concept mean and what formulas are used to calculate it?
Introduction
If you place a dipole in the space of a uniform electric field, you can imagine it as lines of force. A dipole is a system in which there are two charges that are identical in parameters, but they are unlike point charges. Moreover, the distance between them will be much less than the distance to any point on the dipole field. The concept of a dipole moment is studied by a school course in electrodynamics (10th grade).
The dipole axis is a straight line that passes through the points of both charges. A dipole arm is a vector that connects a charge and at the same time is directed from negatively charged particles to particles positively charged. An electric dipole is characterized by the presence of a state such as dipole or electric moments.
By definition, the dipole moment is a vector that is numerically equal to the product of the dipole charge on its shoulder. Moreover, it is aligned with the dipole shoulder. With zero equality of the sum of forces, we calculate the value of the moment. The angle that exists between the dipole moment and the directivity of the electric field is characterized by the presence of a mechanical moment.
Often people find it difficult to calculate the module acting on the structure of the dipole. Here it is necessary to consider the features of calculating the angle "Alpha". It is known that a dipole deviates from a balanced position. But the dipole moment itself is characterized by a restoring character, since it is inclined to be in motion.
Calculations
When this dipole moment is placed in a medium of an inhomogeneous electric field, a force inevitably arises. In such an environment, the indicators of the sum of forces will not be zero. Therefore, there are forces acting on the dipole moment with a point character. The size of the dipole arm is much smaller.
The formula can be written as follows: F = q (E2 - E1) = qdE, where d is the differential of the electric field.
Search for characteristics of the studied physical concept
Consider the topic below. In order to determine what is the characteristic of the electric field, if it is created using a system of charges and is localized in a small space, it is necessary to perform a number of calculations. An example is represented by atoms and molecules, which in their composition have electrically charged nuclei and electrons.
If it is necessary to search for a field at a distance greater than the sizes that make up the particle location region, we will use a number of exact formulas that are highly complex. It is possible to use simpler approximate expressions. Suppose that point sets of charges q k take part in creating an electric field. They are located in a small space.
To perform the calculation of the characteristic that the field has, it is allowed to combine all the charges of the system. Such a system is considered in the form of a point charge Q. The indicators of magnitude will be the sum of the charges that were in the original system.
Location of charges
Imagine that the location of the charge is indicated at any place where the q q charge system is located. When making changes to the location, if it has limits expressed by a small area, such an effect will be insignificant, almost not noticeable for the field at the point of consideration. Within such limits of the approximation of intensity and potential that the electric field has, definitions are made using traditional formulas.
With a zero sum of the total charge of the system, the parameters of the indicated approximation will look rough. This gives reason to conclude that the electric field is simply absent. If it is necessary to obtain a more accurate approximation, separate groups of positive and negative charges of the system under consideration are mentally collected.
If their “centers” shift relative to others, the field parameters in such a system can be described as a field that has two point charges of equal magnitude and opposite in sign. It is noted that they are biased in relation to others. To provide a more accurate characterization of the charge system by the parameters of this approximation, it will be necessary to study the properties of a dipole in an electric field.
Introduction of the term
Back to the definition. An electric dipole is the definition of a system that has two point charges. They have the same size and opposite signs. Moreover, such signs are located at small distances relative to other signs.
You can calculate the characteristics of the process that is created by means of a dipole, and it is represented by two point charges: + q and −q, and they are located at a distance relative to the others.
Calculation sequence
To begin with, we calculate the potential and tension that a dipole has on its axial surface. This is a straight line that runs between two charges. Given the location of point A at a distance that is equal to r relative to the central part of the dipole, and if it is r >> a, using the principle of superposition for the field potential at this point, it will be rational to use the expression to calculate the parameters of the electric dipole.
The value that the tension vector has is calculated by the principle of superposition.
To calculate the field strength, the concept of the ratio of potential and field strength is used:
E x = −Δφ / Δx.
Under such conditions, the direction of the tension vector is indicated longitudinally relative to the axis of the dipole. To calculate its module, the standard formula is applicable.
Important clarifications
It should be borne in mind that the attenuation of the electric dipole field occurs faster than it experiences a point charge. The dipole field potential decreases in inversely proportional direction with respect to the square of the distance, and the field strengths in inversely proportional with respect to the distance cube.
Using similar, but more cumbersome methods, the parameters of the potential and field strength of the dipole are found at arbitrary points, the position parameters of which are determined using such a calculation method as polar coordinates: the distance to the center of the electric dipole (r) and angle (θ).
Tension vector calculations
The concept of tension vector E is divided into two points:
- Radial (E r ), which is directed in the longitudinal direction relative to the straight line.
- Such a straight line connects the indicated point and the center of the dipole with E θ perpendicular to it.
Such a decomposition of each component is directed along the course of change, which occurs with all the coordinates of the point for observation. You can find it by the ratio that connects the field strength indicators with potential modifications.
Finding the vector component at the field strength, it is important to establish the nature of the relationship in the potential changes that occur due to the shift of the observation point in the direction of the vectors.
We calculate the perpendicular component
When performing this procedure, it is important to take into account that the expression of the quantity at a small perpendicular offset will be determined by changing the angle: Δl = rΔθ.
The parameter values for this field component will be equal.
Having obtained the relation, it is possible to determine the field of the electric dipole at an arbitrary point to construct a picture with the field lines of this field.
It is important to consider that all formulas for determining the potential and field strength of a dipole operate only on the product of the quantities that a single dipole charge has and the distance between them.
Dipole moment
The name of the described work is a complete description of the electrical type of properties. It is called the "dipole moment of the system."
By the definition of a dipole, which is a system of point charges, we can find out that it is characterized by the presence of axial symmetry, when the axis is a straight line that passes through several charges.
To specify the full characteristic of the dipole, indicate the direction of orientation, which has an axis. For simplicity of calculations, you can set the vector of the dipole moment. The value of its magnitude is equal to the magnitude of the dipole moment, and the direction vector differs in its coincidence with the axis of the dipole. So, p = qa if a is the direction of the vector that connects the negative and positive charges of the dipole.
The use of such a dipole characteristic is convenient and makes it possible in most cases to simplify the formula and give it the form of a vector. The description of the potential of the dipole field at a point of arbitrary direction is written in the form of a vector.
The introduction of concepts such as the vector characteristic of a dipole and its dipole moment can be carried out using a simplified model - a point charge in a homogeneous field, which includes a system of charges, the geometric dimensions of which do not have to be taken into account, but it is important to know the dipole moment. This is a prerequisite for performing calculations.
How does a dipole behave
The behavior of the dipole can be considered as an example of such a situation. The position of two point charges has a fixed nature of the distance relative to each other. They were placed in a dipole condition of a uniform electric field. Made observations on the process. In physics lessons (electrodynamics), this concept is considered in detail. From the field to the charge, the action of forces is performed:
F = ± qE
They are equal in magnitude and opposite in the nature of the direction. The total force that acts on the dipole is zero. Since such a force has an effect on various points, the indicator of the total moment will be:
M = Fa sin a = qEa sin a = pE sin a
at α, which is the angle connecting the field strength vectors and the dipole moment vectors. Due to the presence of the force moment, the tendency of the dipole moment of the system arises to return to the directions of the electric field intensity vector.
An electric dipole is a concept that is important to clearly understand. You can read more about it on the Internet. It can also be studied in physics classes at school in grade 10, as we discussed above.