Superposition Principle and Continuous Charge Distribution

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Introductions to Superposition Principle and Continuous Charge Distribution

In the field of Electrostatics, which is a sub-concept of physics, we have a superposition principle. It is vital and plays a dominant role. So, let us try to understand what is the principle of superposition in detail. Like it's a definition, extended topics of the superposition principle.


Define the Principle of Superposition

The principle of superposition definition helps us calculate the force uncharted, due to which the force can be caused by other charged particles that are acting on it. It also states that every charged particle creates some electric field, but the electric field is not dependent on any charged particles, whether they are present or absent. The principal also works on the combination of two or more electric fields. This electric field can be calculated by using the formula of coulomb's law. 


Principle of Superposition of Charges 

To explain the principle of superposition in electrostatics, it is better to perform an activity so that the principal can be understood and experienced through a practical.

Let us consider one positive energy, two negative energies. These may exert force on it, which creates electric charges. According to the principle of superposition,

The resultant force is the vector sum of all the forces acting on the body. This can be represented as,

\[\overrightarrow{F_{r}}\] = \[\frac{1}{4 \pi \varepsilon }\] \[[\frac{Qq_{1}}{r_{12}^{2}}\widehat{r}_{12}+\frac{Qq_{2}}{r_{13}^{2}}\widehat{r}_{13}]\]

Where,

\[\widehat{r}_{12}\] and \[\widehat{r}_{13}\] are the unit vectors along the direction of q1 and q2.

∈ is the permittivity constant for the medium in which the charges are placed?

Q, q1, and q2 are the magnitudes of the charges respectively.

r12and r13  are the distances between the charges Q and q1  &  Q and q2 respectively. 

Using this formula for the superposition principle in electric field intensity, we can calculate the force of multiple charged particles. This is the Principle of Superposition. It can be seen in the following figure.

(Image to be added soon)


Continuous Charge Distribution

Along with the superposition principle in electrostatics, we need to get an idea about charge distribution. We know that we will get at least one charged atom, either it is positive or negative. This released the charged element is known as the proton. While the quantization of these protons, it is clear that the gap between them is very less and they are very closely bonded. So, here the charge distribution in them can be explained by stating the principle of superposition as follows in three ways. They are- 

  • Linear charge distribution.

  • Surface charge distribution.

  • Volume charge distribution.

Linear charge distribution: The name itself specifies that the charge distribution will be in linear form. The charge is distributed uniformly to the entire path, whether it is a straight line or a circle. For circles, it is like the circumference of the circle. This linear charge distribution can be denoted byλ. Coulomb's per meter is its measurement. it's formula is, 

λ = dp/ dq .

Surface charge distribution:- If the charge can be distributed among the protons for a specific surface or a specific area of the hole, then it is called surface charge distribution. It is like a partial distribution. It can be measured as coulombs per square meter. It is denoted by σ. 

Volume charge distribution:- the third Way of quantizing charge distribution using the principle of superposition of electrostatic forces. Here the charge can be distributed throughout the volume of the surface. These are majorly observed in cylinders, Spears, etc., its measuring unit is columns per cubic meter. It is denoted by ρ.

If we observe one thing, the linear charge distribution is a straight line. So, the measuring unit is columns per meter. The next one is surface charge distribution, which applies to two-dimensional figures. So, it measures a unit of coulombs per square meter. Finally, the last one volume charge distribution can be used in three-dimensional figures like a sphere, cylinder, cone, etc. Hence the measuring unit is columns per cubic meter.


Conclusion

The principle of superposition in electrostatics for charges can be used to calculate the force applying on them. We also cover the charge distribution on those particles in three different ways. So, all the factors like wavelength, frequency, force, shape everything is countable and considerable.

FAQ (Frequently Asked Questions)

1. What is electrostatics? What is its Significance?

Electrostatics is a branch of Physics. Especially,  enhancement of classical physics. It majorly concentrates on explaining the electric charges exerted by the elements of Coulomb's law, superposition principle, charge distribution, electric fields, magnetic field, electrostatic waves, and many more.

It helps to calculate wavelength and force. It is used to quantize the output. It is used to detect two or more charges at a time. It is good in accuracy, flexibility, etc. With the development of electrostatics only, today we can understand the movement of protons, electrons, energy levels, etc. It is beneficial in many ways.

2. What are the limitations of Coulomb's law?

Besides several advantages of Coulomb law, we also have certain limitations as the second side of a coin. They are- 

  • The coulomb law is not applicable for extended bodies. It is only restricted to point charge distribution.

  • The experiments had been made using the Coulomb law between the nuclear distribution of distance away from 10-15. one cannot assure about the distance below this.

  • The coulomb law can opt for stationary charges only.

  • According to a small exceptional case of Colombia, it can also be applied for extended bodies and a considerable distance. If the distance means slight changes, it fails to calculate.

These are the limitations of Coulomb's law.

3. What do you mean by point charge distribution?

If the charge can be distributed to a specific point without considering the direction travelled, area, volume, etc., then it is known as point charge distribution. It is very rarely used. On the other hand, we have the linear charge distribution, volume charge distribution; surface charge distribution is widely used for different shapes of different dimensions.