Area vector
Definition
An area vector is a vector that represents both the magnitude and the orientation of a surface area. Its magnitude is equal to the area, and its direction is perpendicular (normal) to the surface.
5 Must Know Facts For Your Next Test
- The direction of an area vector is always perpendicular to the surface it represents.
- The magnitude of an area vector corresponds to the actual area of the surface.
- In closed surfaces, area vectors point outward from the enclosed volume.
- Area vectors are crucial in calculating electric flux using Gauss's Law.
- When dealing with non-flat surfaces, they can be divided into infinitesimal elements each with its own area vector.
Review Questions
- What determines the direction of an area vector?
- How is the magnitude of an area vector related to its corresponding surface?
- Why are area vectors important when applying Gauss's Law?
"Area vector" appears in:
Related terms
Electric Flux: The measure of the electric field passing through a given surface, calculated as $\Phi_E = \mathbf{E} \cdot \mathbf{A}$ where $\mathbf{A}$ is the area vector.
Gauss's Law: A fundamental law stating that the total electric flux through any closed surface is equal to $\frac{Q_{enc}}{\epsilon_0}$, where $Q_{enc}$ is the enclosed charge.
Surface Integral: An integral used to calculate quantities over a surface by summing contributions from infinitesimal elements represented by their respective area vectors.
