Continuous charge Distribution: We have read about the arrangements consisting of discrete charges like Q1, Q2,…, and Qn, observing that the operations occupied in these cases were easier and notions of scalar addition could be easily applied there.
However, we are aware that sometimes we have to deal with arrangements where assuming discrete charges is not an alternative.
Here, we have to assume the charges as those which are constantly divided over a surface, length, or volume.
For instance, if we are experimenting with a surface having a continuous charge distribution in the body over its surface, the calculation of electric field value is not possible because of microscopic charged components.
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We instead assume an area section, very tiny but big enough to have multiple such charged components, which we denote as Δs.
Picture
Let us say that the total charge in this area section is equal to ΔQ and the charge density of the object can be expressed as
The unit of σ is C/m2 or Coulomb per square meter.
In the same way, in the case of charge distribution in a body with a line segment of length like a small line part of the wire, the linear charge density can be expressed as
When ΔQ is the charge in that line object. The unit of σ is λ is C/m or Coulomb per meter.
In the same way, when the charge ΔQ is divided over a very small, volume object ΔV, the volume charge density can be expressed as
The unit of ρ is C/m3or Coulomb per cubic meter.
Also read:
Electric Charges and Static Electricity
Electric Charge
Conductors and Insulators
Basic Properties of Electric Charge
Forces between Multiple Charges
Charging by Induction
Magnetic effect of Electric Current
Electric Flux
Electric Dipole
Potential energy of a dipole in an external field
Assume one such object of volume Δv whose charge density is expressed by ρ. Let the distance of the volume element from the point P can be expressed as r.The charge in the volume object can be expressed asρΔv.
According to Coulomb’s Law, the electric field due to charge ρΔv can be expressed as
Here, r is the distance between the charged object and the point P at which the field is to be determined and is the unit vector in the direction of the electric field from the charge to the point P.
According to the principle of superposition, the electric field because of the total charge distribution in a body, divided into various such volume objects can be expressed as
Candidates can refer to the information given above about continuous charge distribution.
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These help you test your own yourself and help you prepare for your exams in a better way.We instead assume an area section, very tiny but big enough to have multiple such charged components, which we denote as Δs.
Picture
Let us say that the total charge in this area section is equal to ΔQ and the charge density of the object can be expressed as
The unit of σ is C/m2 or Coulomb per square meter.
In the same way, in the case of charge distribution in a body with a line segment of length like a small line part of the wire, the linear charge density can be expressed as
When ΔQ is the charge in that line object. The unit of σ is λ is C/m or Coulomb per meter.
In the same way, when the charge ΔQ is divided over a very small, volume object ΔV, the volume charge density can be expressed as
The unit of ρ is C/m3or Coulomb per cubic meter.
Also read:
Electric Charges and Static Electricity
Electric Charge
Conductors and Insulators
Basic Properties of Electric Charge
Forces between Multiple Charges
Charging by Induction
Magnetic effect of Electric Current
Electric Flux
Electric Dipole
Potential energy of a dipole in an external field
Calculation of Electric Field
Let us assume a case when a continuous charge is distributed in a body. Here, we will determine the electric field because of this charge at point P. We can say that the charge density at diverse volumetric objects can be different. Therefore, we divide the body into diverse objects in such a way that the charge density for a specific object can be considered to be a permanent quantity.Assume one such object of volume Δv whose charge density is expressed by ρ. Let the distance of the volume element from the point P can be expressed as r.The charge in the volume object can be expressed asρΔv.
According to Coulomb’s Law, the electric field due to charge ρΔv can be expressed as
Here, r is the distance between the charged object and the point P at which the field is to be determined and is the unit vector in the direction of the electric field from the charge to the point P.
According to the principle of superposition, the electric field because of the total charge distribution in a body, divided into various such volume objects can be expressed as
What are the types of continuous charged distributions?
Types of continuous charged distributions are
- Surface charged distribution
- Linear charged distribution
- Volume distribution of charge
What is symmetrical charge distribution?
A symmetrical charge distribution is considered when a couple of geometrical modifications such that these modifications do not influence any physical change.
How are electric charges divided within an atom?
Subatomic particles have electric charges. Electrons have a negative charge, and protons have a positive charge in the nuclei of atoms.
What is continuous charged distribution?
In a continuous charge distribution, all the charges are strongly bounded together, i.e., having verses space between them. However, this strongly bounded arrangement does not depict that the electric charge is constant. It reflects that the distribution of different charges is continuous, with little space between them.
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