Find the electric field due to an infinite plane of positive charge with uniform surface charge density.
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To find the electric field due to an infinite plane of positive charge with uniform surface charge density, you can use Gauss's law or the method of integration. Here, I will explain the method using Gauss's law.
Gauss's law states that the electric flux through any closed surface is proportional to the total charge enclosed by that surface. In this case, we can imagine a Gaussian surface (a closed surface) that is a flat cylinder with one end inside the plane of charge and the other end outside.
To solve this problem, we first need to determine the charge enclosed by our Gaussian surface. Since the charge density is uniform, we can calculate the charge enclosed by multiplying the surface charge density (σ) by the area of the Gaussian surface (A).
Once we know the charge enclosed, we can apply Gauss's law to find the electric field. Gauss's law states that the electric flux (Φ) through the Gaussian surface is equal to the total enclosed charge (Q_enclosed) divided by the electric constant (ε₀).
Φ = Q_enclosed / ε₀
Since the electric field is uniform and perpendicular to the plane of charge, the electric field lines passing through the two flat circular faces of the Gaussian surface are parallel and of equal magnitude. This implies that the flux through the two faces cancels each other out, and the only contribution to the flux comes from the curved part of the Gaussian surface.
The electric field is therefore given by:
Φ = E * A = Q_enclosed / ε₀
Where E is the magnitude of the electric field and A is the area of the curved surface of the Gaussian cylinder. Solving for E, we get:
E = σ / (2 * ε₀)
So, the electric field due to an infinite plane of positive charge with uniform surface charge density is given by E = σ / (2 * ε₀).
You can refer to the provided link for a visual representation of this concept.