There are 6.25 x 1018 electrons accumulated at a certain point in space. Determine the charge at the point, electric field, electric potential and electric flux at a distance 1 cm from the charge.
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Answer:
1.0 Statement of Equation
The following Electrostatic Field equations will be developed in this section:
Integral form
Differential forms
Maxwell’s first equation is based on Gauss’ law of electrostatics published in 1832, wherein Gauss established the relationship between static electric charges and their accompanying static fields.
The above integral equation states that the electric flux through a closed surface area is equal to the total charge enclosed.
The differential form of the equation states that the divergence or outward flow of electric flux from a point is equal to the volume charge density at that point.
1.1. Maxwell’s Equation No.1; Area Integral
We will derive the integral equation by considering the summation of electric flux density on a surface area, and then as a summation of volume containing electric charge. The two integrals are shown to be equal when they are based on the same charge. Two examples using the equations are shown.
1.1.1 Gauss’ Law
Gauss’ electrostatics law states that lines of electric flux, fE, emanate from a positive charge, q, and terminate, if they terminate, on a negative charge. The space within which the charges exert their influence is called the electrostatic field.
The sketch in Figure 1.1 represents the charges and the three dimensional field. The field is visualized as being made up of lines of flux. For an isolated charge, the lines of flux do not terminate and are considered to extend to infinity.
To obtain the equation relating an electric charge q, and its flux f E, assume that the charge is centered in a sphere of radius r meters. The electric flux density, D, is then equal to the electric flux emanating from the charge, q, divided by the area of the sphere.
coulombs per square meter; where the area is perpendicular to the lines of flux. (One coulomb is equal to the magnitude of charge of 6.25 X 1018 electrons.) The charge enclosed in the sphere is then equal to the electric flux density on its surface times the area enclosing the charge.
q (coulombs enclosed) = D x 4 r2.
The lines of flux contributing to the flux density are those that leave the sphere perpendicular to the surface of the sphere. This leads to the integral statement of this portion of Gauss’ law;
Maxwell’s first equation is based on Gauss’ law of electrostatics published in 1832, wherein Gauss established the relationship between static electric charges and their accompanying static fields.
The above integral equation states that the electric flux through a closed surface area is equal to the total charge enclosed.
The differential form of the equation states that the divergence or outward flow of electric flux from a point is equal to the volume charge density at that point.