Electric Field due to Infinite Wire
Consider a wire that is infinitely long and has a linear charge density λ. To compute the electric field, we utilize a cylindrical Gaussian surface. The flux through the end of the surface will be 0 since the electric field E is radial. Because the electric field and the area vector are perpendicular to each other, this is the case. We may argue that the electric field’s magnitude will be constant since it is perpendicular to every point on the curved surface.
The curved cylindrical surface has a surface area of 2πrl. The electric flux flowing through the curve is equal to E × (2πrl).
According to Gauss’s Law:
ϕ = q ⁄ ε0
E × (2πrl) = λl ⁄ ε0
Hence, Electric Field due to Infinite Wire is given as
E = λ ⁄2πε0r
It’s important to note that if the linear charge density is positive, the electric field is radially outward. If the linear charge density is negative, however, it will be radially inward.
Applications of Gauss’s Law
Gauss’s Law states that the total electric flux out of a closed surface equals the charge contained inside the surface divided by the absolute permittivity. The electric flux in an area is defined as the electric field multiplied by the surface area projected in a plane perpendicular to the field. Now that we’ve established what Gauss law is, let’s look at how it’s used. Application of Gauss Law is important for Class 12 students.
In this article, our main focus is on the Application of Gauss Law with a brief discussion of Gauss Law.
Table of Content
- What is Gauss Law?
- Applications of Gauss Law
- Electric Field due to Infinite Wire
- Electric Field due to Infinite Plane Sheet
- Electric Field due to Thin Spherical Shell
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