Magnetic Fields and Biot-Savart Law

Vocabulary flashcards covering the concepts, equations, and terminology for magnetic field calculation from a current-carrying conductor.

Magnetic Field

A field produced by moving charges or electric current.

Gauss Law

A law used to calculate electric fields when charge distributions possess high symmetry.

Coulomb's Law

A law used to calculate electric fields for low symmetry charge distributions, where the force decreases as $\frac{1}{r^2}$.

Boyle's Severt Law

A law named after two scientists used to calculate the magnetic field produced by moving charges or electric currents with low symmetry.

Ampere's Law

A law used to calculate magnetic fields for current distributions having high symmetry.

Current Element Vector ($d\mathbf{s}$)

A small length element of a wire conductor, denoted as $d\mathbf{s}$ or $d\mathbf{l}$, made into a vector by directing it along the flow of electric current.

Unit Vector ($\hat{r}$)

A vector designated with a cap indicating direction along the distance of $r\,\text{m}$ toward observation point $p$.

Cross Product ($d\mathbf{s} \times \hat{r}$)

The vector product producing a resultant vector perpendicular to the plane containing $d\mathbf{s}$ and $\hat{r}$, defining the direction of the magnetic field.

Proportionality Constant ($k_m$)

The constant replacing the proportionality sign in the magnetic field equation, equal to $\frac{\mu_0}{4\pi}$.

Infinite Conductor Angular Limits

The integration limits for an infinitely long straight wire where $\theta_1$ approaches $0$ and $\theta_2$ approaches $180^\circ$ ($\pi$), evaluating to $\cos(0) - \cos(\pi) = 1 - (-1) = 2$.

Compass Needle

An instrument traditionally kept by sailors that responds to Earth's magnetic field and indicates the presence and direction of a magnetic field.

Magnetic Field Lines

Circular lines used to visualize the magnetic field around a straight conductor, oriented either clockwise or counterclockwise depending on the current's direction.