Magnetic Fields - AP Physics C: Electricity and Magnetism

$F = 24N$. Using $F = qvB$ with $\sin 90° = 1$ for perpendicular motion.

$B = \mu_0 n I$. Field uniform and strongest along central axis of solenoid.

Number of turns per unit length. Higher turn density creates stronger magnetic field inside solenoid.

Voltage generated across a conductor by a magnetic field. Charge separation creates voltage perpendicular to current and field.

$\tau = \mu \times B$. Cross product gives torque magnitude and direction for dipole alignment.

$B = \frac{\mu_0 I}{2R}$. Field strength inversely proportional to loop radius at center.

$F = qvB , \sin \theta$. Force depends on charge, velocity, field strength, and angle between $\vec{v}$ and $\vec{B}$.

Tesla (T). Named after Nikola Tesla, equals $1 , \text{Wb/m}^2$.

Centripetal force causing circular motion. Magnetic force always perpendicular to velocity provides centripetal acceleration.

$E = cB$. Electric and magnetic fields perpendicular in electromagnetic waves.

Keeps charged particles in circular paths. Magnetic force provides centripetal acceleration for circular particle motion.

$F = 9.6 \times 10^{-14} N$. Using $F = qvB$ with electron charge $e = 1.6 \times 10^{-19}$ C.

Right-hand rule: velocity and magnetic field directions. Cross product $\vec{v} \times \vec{B}$ determines force direction.

Zero force as velocity is zero. Magnetic force requires velocity; no motion means no force.

Weber (Wb). Equivalent to tesla-meter squared ($\text{T}\cdot\text{m}^2$).

A torque aligns the dipole with the field. Magnetic torque tends to align dipole moment with field direction.

$\Phi_B = \int \vec{B} \cdot d\vec{A}$. Dot product integrates normal component of field over surface area.

$F = q(E + v \times B)$. Total electromagnetic force combines electric and magnetic components.

No force is exerted on a stationary charge. Magnetic force requires motion; stationary charges experience no magnetic force.

From north pole to south pole outside the magnet. Field lines form closed loops, never intersect, and show field direction.

$\mu = IA$. Product of current and enclosed area gives magnetic moment strength.

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

Thumb: current direction; fingers: magnetic field lines. Force direction given by palm when thumb and fingers align correctly.

$F = ILB , \sin \theta$. Force on wire depends on current, length, field strength, and angle.

Magnetic force is perpendicular to velocity; electric force is not. Key difference: magnetic force always perpendicular to motion.

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

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

Induced EMF opposes change in magnetic flux. Consequence of energy conservation in electromagnetic induction.

Along the axis of the solenoid. Current creates uniform field parallel to solenoid axis inside.