Posted by Mary on Monday, September 24, 2007 at 10:11pm.
A cube is located with one corner at the origin of an x, y, z, coordinate system. One of the cube's faces lies in the x, y plane, another in the y, z plane, and another in the x, z plane. In other words, the cube is in the first octant of the coordinate system. The edges of the cube are 0.20 m long. A uniform electric field is parallel to the x, y plane and points in the direction of the +y axis. The magnitude of the field is 1500 N/C. Find the electric flux through each of the six faces of the cube.
a. bottom face (N·m2/C)
b. top face( N·m2/C)
c. each of the other four faces( N·m2/C)
For Further Reading
Physics - bobpursley, Monday, September 24, 2007 at 10:27pm
flux= integral E.dA or E Area perpendicular to the E field. Each side has an area of .04m^2. So if the E field is in y direction, you deal with the xz planes.
Sketch the cube, if the E is going inward, the flux is negative, outward positive.
I am confused!!!
I tried working this problem but I think my answer is incorrect. Please check it for me.
flux = E.dA
flux = 250 N/C x 0.04m^2
flux = 10 (for each of the faces)
To find the electric flux through each face of the cube, you can use the formula flux = E * dA, where E is the magnitude of the electric field and dA is the area perpendicular to the electric field.
In this case, the electric field is parallel to the x, y plane and points in the direction of the +y axis. Since the cube is oriented such that one face lies in the x, y plane, you will only need to consider the faces in the x, z plane for the calculation of flux.
Each face of the cube has an area of 0.04 m^2. Therefore, the electric flux through each face can be calculated as follows:
a. To find the electric flux through the bottom face (which is in the x, z plane), the area is perpendicular to the electric field. So the flux would be negative, i.e., -1500 N/C * 0.04 m^2 = -60 N·m^2/C.
b. To find the electric flux through the top face (also in the x, z plane), the area is also perpendicular to the electric field. So the flux would be positive, i.e., 1500 N/C * 0.04 m^2 = 60 N·m^2/C.
c. To find the electric flux through each of the other four faces (also in the x, z plane), the area is not perpendicular to the electric field. Therefore, the electric flux through these faces will be zero, as the dot product of E and dA will be zero.
So the final results are:
a. The electric flux through the bottom face is -60 N·m^2/C.
b. The electric flux through the top face is 60 N·m^2/C.
c. The electric flux through each of the other four faces is 0 N·m^2/C.
I apologize for any confusion caused earlier. The flux through each face is not 10, as you had calculated, but it depends on the orientation of the face with respect to the electric field.