Calculation of Electric Flux

Electric flux depends on the angle between the electric field and the surface's normal vector. When field lines are parallel to the normal, flux is maximum and positive. When perpendicular, flux is zero. For a positive charge enclosed in a sphere, field lines point outward, creating positive flux. For a negative charge, field lines point inward, creating negative flux.

When no charge exists inside a closed surface, every electric field line entering the surface must exit somewhere else. The negative flux entering equals the positive flux leaving, resulting in zero net flux. This occurs because electric field sources lie outside the enclosed volume, so field lines cannot terminate inside.

Increasing the enclosed charge increases the electric field magnitude, which directly increases electric flux through the surface. For example, a 1-meter radius sphere enclosing a 10 microcoulomb positive charge produces greater flux than one enclosing a smaller charge, since flux is proportional to the enclosed charge.

Electric flux is calculated using the dot product of the electric field and surface area vector. For a sphere with parallel field lines and area vector, the angle between them is zero. Multiply the electric field magnitude by the sphere's surface area and the cosine of the angle to find the total flux passing through.

In a uniform field between parallel conducting plates, flux through the bottom face is negative because the field opposes the normal vector. Flux through the top face is positive as field and normal align. Flux through side faces is zero since the field is perpendicular to their normals, resulting in zero net flux.

Flux cancels because electric field sources exist outside the box. Field lines entering the box must exit through another face since no charge inside terminates them. The inward flux through one face equals the outward flux through another, producing zero net flux through the entire closed surface.

A positive enclosed charge produces outward-pointing electric field lines and positive flux through the surface. A negative enclosed charge produces inward-pointing field lines and negative flux. The sign of flux directly reflects the sign of the enclosed charge, making flux a useful indicator of charge presence.