Normal vector

Definition

A normal vector is a perpendicular vector to a surface at a given point. In physics, it is often used to calculate flux through surfaces.

5 Must Know Facts For Your Next Test

1. The normal vector is essential in defining the orientation of a surface for calculating electric flux.
2. In Gauss's Law, the direction of the normal vector determines whether the flux is positive or negative.
3. The magnitude of the normal vector does not affect calculations involving Gauss's Law; only its direction matters.
4. For closed surfaces, outward-pointing normal vectors are conventionally used.
5. Normal vectors are often represented by unit vectors to simplify calculations.

Review Questions

• What role does the normal vector play in calculating electric flux?
• How does the direction of a normal vector influence the sign of electric flux according to Gauss's Law?
• Why are unit vectors commonly used as normal vectors in calculations?

Related terms

Electric Flux:

A measure of the quantity of electric field passing through a given surface.

Gauss's Law:

$\Phi_E = \frac{Q_{enclosed}}{\varepsilon_0}$, which relates the electric flux through a closed surface to the charge enclosed by that surface.

Surface Integral:

$\iint_S \vec{E} \cdot d\vec{A}$, representing the integral of a vector field over a surface, crucial for calculating total flux.