[Physics Class Notes] on Superposition Principle and Continuous Charge Distribution Pdf for Exam

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 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}{4pivarepsilon}][[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.

 

 

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 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.

 

Linear Charge Distribution

The linear charge distribution is when charges are dispersed equally along a length, such as around the circumference of a circle or along a straight wire. The symbol for linear charge distribution is.

It is measured in Coulombs per meter and is [lambda =frac{text {dq}}{text{dl}}].

Surface Charge Distribution

Surface charge distribution: A surface charge distribution occurs when a charge is dispersed across a specified region, such as the surface of a disk, and is symbolized by the Greek letter σ.

The distribution of surface charges is determined. Cm^-2 is the unit of measurement or coulombs per square meter.

Volume Charge Distribution

When a charge is spread evenly throughout a volume, such as inside a sphere or a cylinder, it is said to be volume charge distribution. It is symbolized by the symbol.

The coulombs per cubic meter, or Cm^-3, is the unit of measurement for the volume charge distribution.

 

Conclusion

The principle of superposition in electrostatics for charges can be used to calculate the force applying to 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.