Electric Charge Enclosed by Gaussian Cylinder on Flat Metal Surface

What determines the amount of charge enclosed by a Gaussian cylinder embedded in a flat metal surface with uniform charge, perpendicular to the surface?

a. the ratio of the surface charge density to the cross-sectional area of the cylinder

b. the ratio of the cross-sectional area of the cylinder to the surface charge density

c. the product of the surface charge density and the cross-sectional area of the cylinder

Answer:

The amount of charge enclosed by a Gaussian cylinder embedded in a flat metal surface with uniform charge, perpendicular to the surface, is determined by the product of the surface charge density and the cross-sectional area of the cylinder.

When we embed a Gaussian cylinder in a flat metal surface with uniform charge, perpendicular to the surface, the amount of charge enclosed by the cylinder is determined by the product of the surface charge density and the cross-sectional area of the cylinder.

Let's break it down step-by-step:

1. A Gaussian cylinder is a hypothetical cylindrical surface that we use in Gauss's law to calculate the electric field or charge distribution. It's important to note that the Gaussian cylinder must be perpendicular to the surface.
2. In this case, we have a flat metal surface with a uniform charge. This means that the charge is spread out evenly across the surface.
3. The amount of charge enclosed by the Gaussian cylinder is determined by the surface charge density, which represents the amount of charge per unit area on the metal surface.
4. The cross-sectional area of the Gaussian cylinder is the area of the circle formed by the intersection of the cylinder and the metal surface.
5. To calculate the amount of charge enclosed by the Gaussian cylinder, we multiply the surface charge density by the cross-sectional area of the cylinder.

For example, if the surface charge density is 10 C/m^2 and the cross-sectional area of the cylinder is 2 m^2, then the amount of charge enclosed by the cylinder would be 20 C (10 C/m^2 x 2 m^2 = 20 C). Therefore, option C is the correct answer.