Glossary
Area Vector
A vector representing a surface, whose magnitude is equal to the area of the surface and whose direction is perpendicular to the surface.
Example:
For a flat square on the xy-plane, its area vector would point along the z-axis, indicating its orientation in space.
Constant Electric Field Flux
The calculation of electric flux when the electric field is uniform (same strength and direction) across the entire surface, using the formula Φ_E = E ⋅ A.
Example:
Determining the constant electric field flux through a flat window pane when a uniform electric field is present, simply by multiplying the field strength by the area and the cosine of the angle.
Dot Product
A mathematical operation between two vectors that results in a scalar quantity, calculated as the product of their magnitudes and the cosine of the angle between them.
Example:
When calculating electric flux, the dot product of the electric field vector and the area vector determines how much of the field passes perpendicularly through the surface.
Electric Flux
A measure of how much an electric field 'flows' through a given surface. It quantifies the number of electric field lines passing perpendicularly through an area.
Example:
Imagine a net catching raindrops; the amount of water passing through the net's opening per second is analogous to electric flux through a surface.
Gauss's Law
A fundamental law in electromagnetism that relates the total electric flux through any closed surface to the net electric charge enclosed within that surface.
Example:
Using Gauss's Law, one can quickly determine the electric field produced by a spherically symmetric charge distribution by relating the flux through a concentric sphere to the enclosed charge.
Negative Flux
Occurs when the electric field lines are generally pointing inwards towards a closed surface or in an opposite direction to the area vector for an open surface.
Example:
If an electric field points directly into a box, the negative flux signifies that field lines are entering the enclosed volume.
Positive Flux
Occurs when the electric field lines are generally pointing outwards from a closed surface or in a similar direction to the area vector for an open surface.
Example:
If an electric field points directly out of a balloon, the positive flux indicates that field lines are exiting the enclosed volume.
Total Electric Flux Calculation (Integral Form)
The method used to calculate electric flux when the electric field is non-uniform or the surface is complex, requiring integration over infinitesimal area elements: Φ_E = ∫ E ⋅ dA.
Example:
To find the total electric flux calculation through a curved, charged surface where the electric field varies, one must sum up the flux through tiny patches using integration.
Zero Flux
Occurs when the electric field lines are parallel to the surface (perpendicular to the area vector), meaning no field lines pass through the surface.
Example:
If an electric field runs perfectly parallel to a wall, the zero flux through the wall means no field lines are penetrating it.