Magnetic Fields - AP Physics 2

$f = \frac{qB}{2\pi m}$. Frequency of circular motion in uniform magnetic field.

$1.26 \times 10^{-5} \text{ T}$. Using $B = \mu_0 n I$ with given turn density and current.

Torque on a current loop in a magnetic field. Current loop rotates in magnetic field producing measurable deflection.

$F = I(L \times B)$. Current $I$ and length $L$ replace charge and velocity in force equation.

$1.26 \times 10^{-5} \text{ T}$. Using $B = \mu_0 n I$ with given turn density and current.

Mass spectrometer. Different masses follow different curved paths in magnetic field.

$F = q(v \times B)$. Cross product shows force is perpendicular to both $v$ and $B$.

Right-hand rule. Point fingers along $v$, curl toward $B$, thumb shows force direction.

Magnetic flux per unit area. Magnetic field $B$ represents flux density through a surface.

$F/L = \frac{\mu_0 I_1 I_2}{2\pi d}$. Force per unit length between parallel current-carrying conductors.

It relates magnetic fields to the currents which produce them. Fundamental law connecting magnetic fields to their current sources.

$F = q(v \times B)$. Cross product shows force is perpendicular to both $v$ and $B$.

$B = \frac{\mu_0 n I}{2\pi r}$. Toroidal geometry confines field within the torus structure.

Right-hand rule. Point fingers along $v$, curl toward $B$, thumb shows force direction.

Torque on a current loop in a magnetic field. Current loop rotates in magnetic field producing measurable deflection.

West. Using right-hand rule: velocity south, field up gives force west.

$4\pi \times 10^{-7} , \text{T}\cdot\text{m/A}$. Fundamental constant relating magnetic field to current.

$B = \frac{\mu_0 I}{2\pi r}$. Field decreases as $1/r$ with distance from wire.

$B = \frac{\mu_0 I}{2R}$. Field at center is half that of infinite solenoid.

$\Phi_B = B \cdot A \cdot \cos \theta$. Flux depends on field strength, area, and orientation angle.

1 Tesla = 1 N/(A·m). Force per unit current per unit length in magnetic field.

$\tau = \mu \times B$. Torque is cross product of magnetic moment and field vectors.

$B = \frac{\mu_0 I R^2}{2(x^2 + R^2)^{3/2}}$. Field strength decreases rapidly with distance from loop center.

$1 \times 10^{-6} \text{ T}$. Using $B = \frac{\mu_0 I}{2\pi r}$ with given values.

$V_H = \frac{IB}{net}$. Hall effect: voltage across conductor in magnetic field.

Current (I). Force is directly proportional to current flowing through conductor.

Perpendicular to both velocity and magnetic field. Cross product in Lorentz force creates perpendicular direction.

$\tau = nIAB \sin \theta$. Torque depends on loop area $A$ and angle $\theta$ with field.

$F = q(E + v \times B)$. Complete Lorentz force including both electric and magnetic components.