Final answer:
Electric flux Φ is found by Φ = E ⋅ A or Φ = E × A × cos(θ) when considering angles between the field and surface normal. For faces of a cube with a normal parallel or anti-parallel to the field, the flux is ± E × A; for a perpendicular face, the flux is zero.
Step-by-step explanation:
The electric flux through a given surface is calculated using the formula Φ = E ⋅ A, where E is the electric field magnitude and A is the area through which the field passes. For a cube face in the plane y = 0, when the normal of the face points outwards and aligns with the electric field, the flux is positive, while for the face in the plane y = l with the normal pointing outwards, the flux is negative if the electric field is in the opposite direction.
The net electric flux through a closed surface, such as a cube, is zero if the number of field lines entering and exiting the surface is equal. To compute the flux through a non-perpendicular plane, one must consider the angle θ between the electric field and the normal to the surface.
The formula becomes Φ = E × A × cos(θ). When the normal makes a 0° or 180° angle with the field, the cosine term equals 1 or -1, leading to Φ = ± E × A. For an angle of 90°, the cosine term is 0 and the flux is zero, indicating no field lines pass through the surface.