(Solved): An infinite, uniform plane charge of surface charge density cuts through a spherical Gaussian su ...

Expert Answer

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To find the electric flux through the Gaussian surface, we need to apply Gauss's law, which relates the electric flux through a closed surface to the charge enclosed within that surface:

? = q/?0

where ? is the electric flux through the surface, q is the charge enclosed within the surface, and ?0 is the electric constant.

In this problem, we have an infinite, uniform plane charge of surface charge density ? cutting through a spherical Gaussian surface of radius r at an angle of ?, where r = R/9 and ? = 120°. We need to find the electric flux through this Gaussian surface.

To apply Gauss's law, we need to find the charge enclosed within the Gaussian surface. The charge enclosed within a Gaussian surface is equal to the product of the surface charge density and the area of the surface. The surface area of a sphere is given by:

A = 4?r^2

where r is the radius of the sphere.

In this problem, the surface area of the spherical Gaussian surface is:

A = 4?r^2 = 4?(R/9)^2 = (4?R^2)/81

The charge enclosed within the Gaussian surface is:

q = ?A = ?(4?R^2)/81