Vector field

Definition

A vector field is a map that assigns a vector to every point in space. In the context of electric fields, it represents the direction and magnitude of the electric force experienced by a positive test charge at each point.

5 Must Know Facts For Your Next Test

1. The electric field vector $\mathbf{E}$ at a point is defined as the force $\mathbf{F}$ per unit charge $q$: $\mathbf{E} = \frac{\mathbf{F}}{q}$.
2. Electric field lines represent the vector field visually, showing the direction of the field; they point away from positive charges and toward negative charges.
3. The strength of an electric field created by a point charge decreases with the square of the distance from the charge: $E = \frac{kQ}{r^2}$, where $k$ is Coulomb's constant.
4. In a uniform electric field, vectors are parallel and equally spaced, indicating constant magnitude and direction throughout the region.
5. Superposition principle applies to vector fields: The total electric field due to multiple charges is the vector sum of individual fields created by each charge.

Review Questions

• How do you calculate an electric field at a point due to a single point charge?
• What does it mean when electric field lines are closer together?
• Explain how you would find the net electric field due to multiple charges using superposition.

Related terms

Electric Field Line: A visual representation of an electric field where each line indicates direction and spacing indicates strength.

Coulomb's Law: $F = k \frac{|Q_1 Q_2|}{r^2}$, describing the electrostatic force between two charges separated by distance $r$.

Gauss's Law:

$\oint \mathbf{E} \cdot d\mathbf{A} = \frac{Q_{\text{enc}}}{\epsilon_0}$, relating electric flux through a closed surface to enclosed charge.