What is the definition of electric flux through a surface?

What is the definition of electric flux through a surface?

• A. Φ_E = ∮ E · dA
• B. Φ_E = ∮ E dA
• C. Φ_E = ∮ dA · E
• D. Φ_E = ∮ E × dA

Answer: (A)

Electric flux through a surface measures how much electric field passes through that surface. To compute it, treat the area element as a vector dA pointing normal to the surface with magnitude equal to the patch area. The dot product E · dA picks out the component of the field that goes through the surface, and integrating this over the whole surface gives the total flux: Φ_E = ∬_S E · dA. For a closed surface, this is written with a closed-surface integral ∮ E · dA. The sign reflects whether E is exiting or entering the surface. Using a cross product would not produce a scalar flux, and omitting the dot product would ignore the field component normal to the surface. This definition underpins Gauss’s law, relating the flux to the enclosed charge.

Electric flux through a surface measures how much electric field passes through that surface. To compute it, treat the area element as a vector dA pointing normal to the surface with magnitude equal to the patch area. The dot product E · dA picks out the component of the field that goes through the surface, and integrating this over the whole surface gives the total flux: Φ_E = ∬_S E · dA. For a closed surface, this is written with a closed-surface integral ∮ E · dA. The sign reflects whether E is exiting or entering the surface. Using a cross product would not produce a scalar flux, and omitting the dot product would ignore the field component normal to the surface. This definition underpins Gauss’s law, relating the flux to the enclosed charge.