A disc has charge distribution sigma and radius R . What is the Electric Field in N/C at a point P , located a distance x directly above the center of the disc?Write your answer in terms of sigma, R ,x , k, and pi (type "pi"). Indicate multiplication with a "*" and division with a "/".

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To find the electric field at point P above the center of the disc, we can use Gauss's Law. Gauss's Law states that the electric field through a closed surface is equal to the charge enclosed divided by the permittivity of free space.

First, let's find the charge enclosed by a disc. The charge density of the disc is given as sigma, which represents the charge per unit area. The area of a disc is given by A = pi * R^2, where R is the radius of the disc.

So, the charge enclosed by the disc can be calculated as Q = sigma * A = sigma * pi * R^2.

Now, let's consider a Gaussian surface in the form of a cylindrical tube with a radius r and height h, centered at point P above the disc. By symmetry, the electric field will be constant on this surface.

The electric flux through the Gaussian surface is simply the electric field at P multiplied by the surface area of the Gaussian surface. The surface area of the Gaussian surface is A = pi * r^2.

According to Gauss's Law, the flux is also equal to the charge enclosed divided by the permittivity of free space, which can generally be written as:
Electric Flux = (Q_enclosed) / (epsilon0).

Since the electric field is constant over the Gaussian surface, we can write the total flux as electric field times surface area:
Electric Field * A = (Q_enclosed) / (epsilon0).

Substituting the values we derived earlier, we have:
Electric Field * (pi * r^2) = (sigma * pi * R^2) / (epsilon0).

Now, we can solve for the electric field at point P:
Electric Field = (sigma * R^2) / (2 * epsilon0 * r^2).

Since the point P is located a distance x directly above the center of the disc, we can substitute r = x into the equation:
Electric Field = (sigma * R^2) / (2 * epsilon0 * x^2).

Therefore, the electric field at point P, located a distance x directly above the center of the disc, is given by:
Electric Field = (sigma * R^2) / (2 * epsilon0 * x^2), where epsilon0 is the permittivity of free space.