Magnetic Fields of Current-Carrying Wires - AP Physics C: Electricity and Magnetism

Magnetic field doubles. Field inversely proportional to distance.

$B = \frac{\mu_0 I}{2 \pi r}$. Derived from Ampere's law for infinite straight wire.

Orientation of magnetic field relative to current. Fundamental geometric relationship in magnetism.

No effect on field strength at a point. Field depends on current and distance, not length.

Magnetic permeability of free space. Fundamental constant relating current to magnetic field.

Tesla (T). Standard SI unit for magnetic flux density.

Concentric circles. Symmetrical circular pattern around the wire.

Uniform and parallel to the solenoid's axis. Interior field is constant and directed axially.

Magnetic permeability of free space. Fundamental constant relating current to magnetic field.

Biot-Savart is used for finite current segments. Biot-Savart applies to any current configuration.

Magnetic field is inversely proportional to $r^2$. Field strength follows inverse square law dependence.

Biot-Savart Law. General law for magnetic field calculations.

Thumb in direction of current, fingers curl in direction of field. Standard method for determining field direction.

Tesla (T). Standard SI unit for magnetic flux density.

$d\mathbf{l}$. Infinitesimal length vector of current path.

$4\pi \times 10^{-7} \text{ T m/A}$. Exact value defined in SI unit system.

Perpendicular to the plane of the loop. Field direction follows right-hand rule convention.

Direction of $dB$ is perpendicular to $d\mathbf{l}$ and $\mathbf{r}$. Cross product determines orientation using right-hand rule.

Number of turns per unit length. Turn density parameter in solenoid formula.

Fingers curl with current, thumb points to field direction. Standard convention for circular current paths.

Perpendicular to velocity and magnetic field. Lorentz force direction from cross product.

Inversely proportional to distance. Field strength decreases as distance increases.

$B = 1.884 \text{ T}$. Using $B = \mu_0 n I$ with given parameters.

Reverses the magnetic field direction. Field direction opposes original direction.

Circular within the core, zero outside. Confined field within toroidal core only.

$B = \frac{\mu_0 I}{2R}$. Field at center uses simplified Biot-Savart result.

$dB = \frac{\mu_0}{4\pi} \frac{I d\mathbf{l} \times \mathbf{r}}{r^3}$. Fundamental law relating current elements to magnetic field.

Calculate magnetic fields from current segments. Used when symmetry doesn't allow Ampere's law.

Summing contributions from current elements. Superposition principle requires vector addition.