Electric flux measures how much electric field passes through a surface. It is useful because it connects a visual idea, field lines crossing an area, to a precise calculation. A surface with more field lines passing through it has greater flux.
Electric flux is especially important for understanding Gauss's law and electric fields around symmetric charge distributions.
For a flat surface in a uniform electric field, flux depends on field strength, surface area, and the angle between the electric field and the area vector. The area vector points perpendicular to the surface, so only the component of the electric field parallel to that vector contributes to flux. If the field is perpendicular to the surface, flux is largest, and if the field runs along the surface, flux is zero.
For closed surfaces, the net electric flux reveals how much charge is enclosed inside.
Key Facts
- Electric flux through a flat surface in a uniform field is ΦE = E A cos θ.
- θ is the angle between the electric field vector E and the area vector A, not the angle between the field and the surface itself.
- The area vector has magnitude A and points perpendicular to the surface.
- Maximum flux occurs when θ = 0 degrees, so ΦE = E A.
- Zero flux occurs when θ = 90 degrees, so ΦE = 0.
- Gauss's law states ΦE,total = q_enclosed / ε0 for a closed surface.
Vocabulary
- Electric flux
- Electric flux is a measure of the amount of electric field passing through a surface.
- Electric field
- An electric field is a vector field that gives the force per unit positive charge at each point in space.
- Area vector
- An area vector is a vector perpendicular to a surface with magnitude equal to the surface area.
- Gauss's law
- Gauss's law states that the net electric flux through a closed surface equals the enclosed charge divided by the permittivity of free space.
- Closed surface
- A closed surface is a surface that completely encloses a volume, such as a sphere, cube, or cylinder with end caps.
Common Mistakes to Avoid
- Using the angle between the field and the surface instead of the area vector. The formula ΦE = E A cos θ uses the angle between E and the normal to the surface.
- Forgetting that flux can be negative. Flux is negative when the electric field points opposite the chosen area vector direction.
- Assuming a larger surface always means larger net flux. For a closed surface, net flux depends on enclosed charge, not simply on surface size.
- Applying ΦE = E A cos θ to a nonuniform field without modification. If the field changes across the surface, the surface must be divided into small pieces or evaluated with an integral.
Practice Questions
- 1 A flat surface has area 0.50 m^2 and is placed in a uniform electric field of 200 N/C. The angle between the field and the area vector is 60 degrees. Calculate the electric flux.
- 2 A square surface of side length 0.20 m is placed so its area vector is parallel to a uniform electric field of 750 N/C. What is the electric flux through the square?
- 3 A closed spherical surface contains no charge, but several electric field lines enter and leave it. Explain why the net electric flux through the sphere is zero even though the electric field at the surface is not zero.