Uniformly Charged Infinite Plane Sheet

The electric force per unit charge, characterizes the electric field. It is another crucial topic for the Class XI examinations, among others. Subjects in the Class XI curriculum are linked to various courses and their ramifications are discussed. The notes on this topic include all elements of studying an infinite evenly charged sheet and the characteristics of the Gaussian Surface. Electric Field Lines are mentioned in the article.

An Infinite Uniformly Charged Sheet 

The electric field determines the direction of the field. We know that when there is a positive charge, the electric field is directed radially outward and when there is a negative charge, the electric field is directed inward. Electric fields are produced by electric charges or by time-varying magnetic fields. Electric fields are one of the four basic forces of nature and one of the primary components of electromagnetic force.

Gauss’s law states that the total electric flux through a closed surface is equal to the total charge divided by the permittivity of free space. We have the gaussian surface and the charged sheet in this query. Given the surface charge density, we can calculate the total charge enclosed by the surface by calculating the area of the charged sheet within the gaussian sphere.

According to the Gauss theorem, the total electric flux through a closed surface is equivalent to the combined charge enclosed by the surface divided by the permittivity of open space.

The electric field lines that travel through a particular surface normal to the electric field are described as electric flux.

• Using Gauss’s law, we may define it mathematically as = Q0.
• Where is the electric flux, Q is the total contained charge and 0 is the free space permittivity.
• In the next section, we will use Gauss’s law to calculate the electric flux across the given surface.
• The total charge encompassed by the gaussian surface must be determined.

The charge density of the sheet is,

• The gaussian surface will encompass a circular region on the sheet. The radius of the circular sheet will be equal to a = 𝜋R2.
• As a result, the area of the circular sheet inside the Gaussian sphere is A =𝜋 a2.
• Q is the charge contained by the gaussian surface.

According to Gauss’ rule, the electric flux via the Gaussian surface is 𝜙 = Q/ϵ0.

The area essential of the electric field across any closed surface is equal to the total charge encompassed by the surface divided by the permittivity of open space, as shown in the integral version of Gauss’s equation. Hence, we may represent it formally as E.dA = Q/ϵ0.

In the preceding illustration, the x-axis denotes the uniform surface charge distribution on an infinite planar sheet that is normal to the provided plane. The electric field is independent of the y and z coordinates and its direction at each place must be parallel to the x-axis.

The Gaussian surface is a rectangular parallelepiped with a cross-sectional area A in the preceding example.

Electric Field 

An electric field may be thought of as a property connected with every location in space where a charge exists in any form. The electric force per unit charge is another way to characterize an electric field.

The electric field formula is as follows:

E is equal to F/Q.

Where,

• The letter E denotes the electric field.
• F is a powerful force.
• The charge is Q.

Changing magnetic fields or electric fields are the most common causes of electric fields.

The direction of the field is assumed to be the direction of the force acting on the positive charge. The electric field extends outward from positive and inward from negative charges.

Definition of Gaussian Surface 

The Gaussian surface is a closed surface in three-dimensional space that may be used to compute the flux of a vector field. These vector fields might be gravitational, electric or magnetic fields. The gaussian surface may be determined using Gauss’ law.

The Gaussian surface is a closed surface in three-dimensional space that may be used to compute the flux of a vector field. These vector fields might be gravitational, electric or magnetic fields. The gaussian surface may be calculated using Gauss law:

Gaussian Surface Formula

Where Q(V) denotes the electric charge stored in V.

A sphere’s Gaussian surface

When any of the following causes a flux or electric field to be formed on the surface of the spherical Gaussian surface:

• A solitary charge
• Homogeneous charge distribution in a spherical shell
• Spherical symmetry in charge distribution

Consider a spherical shell S with uniform charge distribution Q, radius R and negligible thickness. Using Gauss’ law, calculate the electric field E at a distance r from the charged shell’s center. Net flow of electric flux through the Gaussian surface is equal to Q/ϵ0.

Electric Field Line 

Electric field lines are a great method to see how electric fields look. Michael Faraday was the one who originally introduced them.

At a location, a field line is drawn tangential to the net. As a result, the tangent to the electric field line at any place corresponds to the direction of the electric field at that location. Second, the relative density of field lines surrounding a place reflects the intensity (magnitude) of the electric field at that location. In other words, if there are more electric field lines in the area of point A than there are in the vicinity of point B, the electric field at point A is stronger.

Electric Field Line Properties

• The electric field lines never cross one another.
• The electric field lines run perpendicular to the charge’s surface.
• Both the amount of the charge and the number of field lines are proportional.
• The point of departure

Conclusion

Consider a charge sheet that is infinitely thin and has a uniform surface charge density. Based on understanding symmetry principles, the electric field lines will originate naturally from this surface. A rectangular parallelepiped with cross-sectional area A would be an appropriate Gaussian surface. Only the two sides will contribute to the flow . Because the electric field lines are perpendicular to the other sides, they do not contribute to the overall flux.