A point charge of 1.8 uC is at the center of a Gaussian cube 55 cm on edge. What is the net electric flux through the surface?
I have no idea where to start with this problem.
To calculate the net electric flux through a closed surface, you need to use Gauss's Law. Gauss's Law states that the electric flux through a closed surface is equal to the total charge enclosed divided by the electric constant, ε0.
Here are the steps to solve this problem:
1. Determine the total charge enclosed by the Gaussian cube. In this case, the point charge of 1.8 uC is at the center of the cube. Since the charge is at the center, it will split evenly into eight smaller cubes of equal volume. So, the charge enclosed by one of these smaller cubes will be (1.8 uC) / 8 = 0.225 uC.
2. Convert the charge enclosed into Coulombs. Recall that 1 microCoulomb (uC) is equal to 1 x 10^-6 Coulombs (C). Therefore, the charge enclosed is 0.225 uC * 1 x 10^-6 C/uC = 2.25 x 10^-7 C.
3. Calculate the surface area of the Gaussian cube. The surface area of a cube can be found by multiplying the length of one side by itself, and then multiplying the result by 6 (since a cube has six faces). In this case, the length of one side is 55 cm, so the surface area is (55 cm)^2 * 6 = 18150 cm^2.
4. Convert the surface area into square meters (m^2). Recall that 1 square meter (m^2) is equal to 10,000 square centimeters (cm^2). Therefore, the surface area is 18150 cm^2 * 1 m^2/10000 cm^2 = 1.815 m^2.
5. Calculate the net electric flux using Gauss's Law. The formula for electric flux is Flux = (enclosed charge) / ε0. The value for ε0, the electric constant, is approximately 8.854 x 10^-12 C^2 / (Nm^2). Therefore, the net electric flux is (2.25 x 10^-7 C) / (8.854 x 10^-12 C^2 / (Nm^2)) = 2.545 x 10^4 Nm^2/C.
So, the net electric flux through the surface of the Gaussian cube is 2.545 x 10^4 Nm^2/C.