Magnetism and Moving Charges - AP Physics C: Electricity and Magnetism

1 T = 10,000 G. Tesla is the larger SI unit; Gauss is the smaller CGS unit.

$\mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B})$. Combined electric and magnetic forces on moving charged particle.

Permeability of free space. Fundamental constant relating magnetic field to current in vacuum.

$r = 0.1 , \text{m}$. Using $r = \frac{mv}{qB}$ with proton mass and given parameters.

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

$B = \frac{\mu_0 N I}{2 \pi r}$. Field inside toroidal coil depends on total turns and radius.

Use right-hand rule: thumb in velocity, fingers in field, palm shows force. Same right-hand rule applies for force direction on positive charges.

Ampere-square meters ($\text{A} \cdot \text{m}^2$). SI unit combining current and area for magnetic dipole strength.

Speed remains constant; direction changes. Magnetic force is always perpendicular to velocity, doing no work.

$u = \frac{B^2}{2\mu_0}$. Energy stored per unit volume in magnetic field.

$\mu_0 = 4\pi \times 10^{-7} , \text{T} \cdot \text{m/A}$. Exact value defined in SI units for magnetic calculations.

$\mu = 0.1 , \text{A} \cdot \text{m}^2$. Multiple turns multiply the effective current-area product.

$F = \frac{\mu_0 I_1 I_2 L}{2\pi d}$. Force per unit length between parallel wires separated by distance $d$.

$d\mathbf{B} = \frac{\mu_0}{4\pi} \frac{I d\mathbf{l} \times \mathbf{r}}{r^3}$. Law for calculating magnetic field from any current distribution.

$F = 3.2 \times 10^{-13} , \text{N}$. Using $F = qvB$ with proton charge $1.6 \times 10^{-19}$ C.

$F = 1.6 \times 10^{-14} , \text{N}$. Using $F = qvB$ for perpendicular motion in magnetic field.

$F = 3 , \text{N}$. Using $F = ILB$ since wire is perpendicular to field.

$B = \frac{\mu_0 I}{2R}$. Field strength at the center of a current loop with radius $R$.

$\Phi_B = \int \mathbf{B} \cdot d\mathbf{A}$. Dot product of magnetic field and area vectors over surface.

$\mu = I A$. Product of current and enclosed area gives magnetic dipole moment.

$B = \mu_0 n I$. Field inside long solenoid is uniform and proportional to turn density.

$B = \frac{\mu_0 I}{2\pi r} = 5 \times 10^{-6} , \text{T}$. Using $B = \frac{\mu_0 I}{2\pi r}$ with given values.

Use right-hand rule: thumb in current direction, curl fingers. Fingers curl in direction of field lines around the current.

Circular or helical, depending on initial velocity. Trajectory depends on initial velocity component parallel to field.

Force is zero. No force when $\sin \theta = 0$ in the force equation.

$F/L = 1 \times 10^{-4} , \text{N/m}$. Using force per length formula with given current and separation values.

$\tau = \mu B \sin \theta$. Torque depends on magnetic moment, field strength, and orientation angle.

No force; the charge remains stationary. Magnetic force requires motion; stationary charges experience no magnetic force.

$B = \frac{\mu_0 I}{2\pi r}$. Field decreases inversely with distance from straight current-carrying wire.