A cube of side a is placed in a uniform field E=6.50 * 10^3 N/C with edges parallel to the field lines.
a) whats the net flux through the cube?
b) what is the flux through each of its six faces?
To find the net flux through the cube, we need to calculate the flux through each face of the cube and then sum them up.
a) The net flux through the cube is the sum of the flux through each face.
b) To find the flux through each face, we can use the formula: Flux = Electric field strength x Area x Cosine of the angle between the normal vector of the surface and the electric field vector.
Since the cube is placed with its edges parallel to the field lines, the angle between the normal vector of each face and the electric field vector is 0 degrees, and the cosine of 0 degrees is 1.
The area of each face of the cube is (side length)^2.
Therefore, to calculate the flux through each face, we can use the formula: Flux = E x A,
where E is the electric field strength and A is the area of the face.
Now, let's calculate the net flux through the cube and the flux through each face:
a) Net Flux through the cube:
Since the cube has 6 faces with the same flux, the net flux is equal to 6 times the flux through each face.
b) Flux through each face:
Flux = E x A
= (6.50 x 10^3 N/C) x (a^2)
= 6.50 x 10^3 a^2 Nm^2/C
Therefore, the net flux through the cube is 6 times the flux through each face, and the flux through each face is 6.50 x 10^3 a^2 Nm^2/C.
To find the net flux through the cube and the flux through each of its six faces, we need to use Gauss's Law. Gauss's Law relates the flux of an electric field through a closed surface to the charge enclosed within that surface.
a) Net Flux Through the Cube:
The net flux (Φ) through the closed surface of the cube can be calculated using Gauss's Law:
Φ = E * A
where Φ is the net flux, E is the electric field strength, and A is the area of the closed surface.
Since the electric field is uniform and the surface of the cube is parallel to the field lines, the net flux through the closed surface of the cube will be the same for all six faces. Therefore, we can calculate the net flux through one face and multiply it by 6 to get the total net flux through the cube.
The area of one face of the cube (A_face) is given by:
A_face = a²
where a is the length of each side of the cube.
Hence, the net flux through the cube (Φ_cube) is given by:
Φ_cube = Φ_face * 6 = E * A_face * 6
= E * a² * 6
b) Flux Through Each Face:
To find the flux through each face of the cube, we use the fact that the net flux through the cube is equally distributed among the six faces.
So, the flux through each face of the cube (Φ_face) is given by:
Φ_face = Φ_cube / 6 = (E * a² * 6) / 6
= E * a²
To obtain the numerical values, substitute the given value for E and the length of the side a into the above equations.
a)Unless the cube has a charge inside, the net flux through all sides is zero, because of Gauss' Law. They should have told you if the cube had a charge inside.
b)The situation is different if the cube is conducting or nonconducting. If there is no charge and no polarization of the cube, the flux through the two faces will be E a^2 and -Ea^2. There will be no flux thourgh the sides.