Continuous Charge Distribution Definition
The continuous load distribution system is a system in which the charge is uniformly distributed over the conductor. For a continuous charging device, the infinite number of charges is closely packed and there is no space between them. Unlike the discrete charging system, the continuous load distribution in the conductor is uninterrupted and continuous. There are 3 types of continuous charge distribution system -
Linear Charge Distribution
Surface Charge Distribution
Volume Charge Distribution
Linear Charge Density
If the charge is not evenly distributed over the length of the conductor, it is called linear charge distribution. It is often referred to as linear charge density and is denoted by the Lambda (λ ) symbol. Mathematically, there is a linear charge density -
λ = dq/ dl
The unit of the linear load density is C / m. If we find a conductor with a length of 'L' with a surface load density of λ and take an aspect of dl on it, then a small charge will be on it.
dq = λ dl
So, there will be an electrical field on the small charge element dq.
dE = kdq/r2
dE = kλdl / /r2
In order to calculate the net electrical field, we will integrate both sides with the correct limit, i.e.
\[\int dE=\int_{0}^{l}\frac{k\lambda dl}{r^2}\]
\[\int dE=\frac{k}{r^2}\int_{0}^{l}\lambda dl\]
Surface Charge Density
When the charge is uniformly distributed over the conductor surface, it is called Surface Charge Density or Surface Charge Distribution. It is denoted by the symbol σ (sigma) and the unit is C / m2. It is also defined as a charge/per area of the unit. Mathematically the density of the surface charge is
σ = dq / ds
Where dq is a small element of charge over a small ds surface. So, there will be a small charge on the driver -
dq = σ ds
The electric field due to a small charge at a distance of 'r' can be evaluated as
dE = kdq/r2
dE = kσdl / /r2
Integrating both sides with proper limits we get
\[\int dE\int_{0}^{s}\frac{k\sigma ds}{r^2}\]
\[\int dE=\frac{k}{r^2}\int_{0}^{s}\sigma ds\]
Volume Charge Density
When the charge is distributed over a driver's volume, it is called Volume Charge Distribution. It is denoted by the ρ (rho) symbol. In other words, the charge per unit volume is called Volume Charge Density and its unit is called C / m3. Mathematically, the density of the volume charge is
ρ = dq/ dv
where dq is a small charge element located in a small volume dv. To find the total charge, we must integrate dq with the correct limits. The electric field due to dq will be
dq = ρ dv
dE = kdq / r2
dE = kρdv / /r2
Integrating both sides with proper limits we get
\[\int dE\int_{0}^{v}\frac{vpdv}{r^2}\]
\[\int dE=\frac{k}{r^2}\int_{0}^{v}pdv\]
Calculation of Electric Field
Let us consider the case of the continuous distribution of charges in the body. Here, because of this charge, we'll measure the electrical field at point P. We can say that the charge density of different volumetric elements can be different so that we divide the body into different elements so that the charge density of a particular element can be considered to be a fixed quantity. Consider one of those elements of volume Δv, the charge density of which is given by ρ. Let the distance between the volume element and point P be given as r. The charge in the volume element could be given as ρΔv. As per the law of Coulomb, the electrical field can be given as ρΔv due to the charge.
\[\Delta E=\frac{1}{4\pi \epsilon _0}\frac{p\Delta v}{r^2}\overbrace{r}\]
Here, r is the distance between the charged part and the point P at which the field is to be measured, and ř is the unit vector in the direction of the electrical field from the charge to point P. By the principle of superposition, the electrical field can be given as a result of the total distribution of the charge in the body, which is divided into a number of such volume elements.
\[E=\frac{1}{4\pi \epsilon _0}\sum_{all\Delta v}\frac{p\Delta v}{r^2}\overbrace{r}\]
Types of Charge Distribution
Electrical field due to the above volume charge distribution (for 1 and n volume elements) will be as follows -
\[\Delta E=\frac{1}{4\pi \epsilon _0}\frac{p\Delta v}{r^2}\widehat{r'}\Delta E\approx \frac{1}{4\pi \epsilon _0}\sum \frac{p\Delta v}{r^2}\widehat{r'}\]
FAQs on Continuous Charge Distribution
1. A rod of length l with uniform charge per unit length λ is placed at a distance d from the origin along the x-axis. A similar rod is placed at the same distance along the Y-axis. Determine the magnitude of net electric field intensity at the origin.
Let's first find Electric field due to the rod on x-axis, say E1
Consider a small length element dx, distance x away from origin.
Field due to this dE1 = kλdx / x2
Integrating from x = d to x = d+l
Gives E1= λl / 4πϵ0d(d+l) along -x direction
Now, E2is along the -y direction and is the same in magnitude.
Thus,
∣E∣ = √2∣E1∣ = √2λl / 4πϵ0d(d+l)
2. What do you mean by continuous charge distribution? Also define uniform and non-uniform charge distribution?
In a continuous distribution of charges, all charges are closely linked together, i.e. they have much less space between them. But this tightly bound system does not mean that the electrical charge is uninterrupted. It is obvious that the distribution of separate charges is continuous, with little space between them.
Uniform Charge Distribution
If the charge is not concentrated in any section but distributed uniformly, then it is considered a uniform distribution of the charge.
Non-uniform Charge Distribution
If the charge is not uniformly spread over the surface, the distribution of the charges is not uniform.
3. What is discrete and continuous charge distribution?
The Distribution charge can be either discrete or continuous depending on the amount of charge distributed or the material of the electric device. We also learned that the charges creating the electric field can have a discrete distribution, if the given charges are at precise points, or a continuous distribution if the given charge is spread out either evenly or unevenly along a particular line, across any surface, or throughout a volume. Students can get more information on the topic from Vedantu. Vedantu is an e-learning portal for the students that helps them in clear understanding of the topics related to their class curriculum.
4.What is the formula of continuous charge distribution?
The formula of the continuous charge distribution is really important to understand the concept even more clearly. The students can refer to any type of formulas or concepts involved in any subject on the Vedantu website and prepare well for their exams. The unit of given λ is calculated as C/m or Coulomb per meter. The unit of ρ is C/m3or Coulomb per cubic meters. Here, r is the particular distance between the specific charged element and the definite point P at which the field is to be calculated and ř is the unit vector in the calculated direction of the electric field from the charge to the point P.
5. What is meant by an electric field of continuous charge distribution?
In a continuous charge distribution, all the charges are closely bound together where the charges have very little space between them. But this closely bound system doesn't mean that the electric charge is uninterrupted; it can be interrupted in various ways but still continuous. It clears that any distribution of separate charges is a continuous process, having only a minor space between them. The electric field at a specific point P due to a charged object is almost approximately given by the sum of the fields at P due to all such charge elements available. If the charge Q is uniformly distributed along the wire of length L, then linear charge density (charge per unit length) will be calculated as λ = Q/L.
6. What does electric field distribution in this chapter mean?
Generally, the electric field distribution means the amount of space available for the electricity to just pass inside any electronically charged device. It mostly differs from one device to another as the size and capacity may differ. It is obtained by solving Poisson's and Laplace's equations under the given boundary conditions. They particularly stated that any specific electric potential is always influenced by the height of gas space, relative permittivity, and charge density.
7. What is the meaning of charge distribution involved in continuous distribution?
The term charge distribution explained in the continuous distribution process is therefore ultimately composed of individually charged particles separated by specific regions containing no charge. For example, the total charge in any particular electrically charged metal object is totally made up of conduction electrons moving randomly in the metal's crystal lattice. There will be space inside the electronic device where the electricity doesn't pass because not all areas inside the electronic device will have the provision to pass on electrons.