Induced Currents and Magnetic Forces - AP Physics C: Electricity and Magnetism

$\text{F} = \text{I} \times \text{L} \times \text{B} \times \text{sin}(\theta)$. Current-carrying wire experiences force in magnetic field.

$\text{F} = \text{q}(\text{v} \times \text{B})$. Cross product gives force perpendicular to both $\vec{v}$ and $\vec{B}$.

$\text{EMF} = -\frac{d\text{Φ}_B}{dt}$. Faraday's law for single loop electromagnetic induction.

$\text{Φ}_B = \text{B} \times \text{A} \times \text{cos}(\theta)$. $\theta$ is angle between $\vec{B}$ and area normal.

Current, magnetic field strength, loop area, angle. Force depends on current, field strength, geometry, and orientation.

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

Induced EMF. Faraday's law links flux change to EMF generation.

Ampere-square meter (A·m²). Product of current and enclosed area for magnetic dipole.

Electric current. Detects small currents through magnetic deflection.

Tesla (T). Also written as Weber per square meter (Wb/m²).

$\text{B} = \frac{\text{μ}_0 \text{n} \text{I}}{\text{L}}$. $n$ is turns per unit length, creates uniform field inside.

Induced current is inversely proportional to resistance. Current equals EMF divided by resistance (Ohm's law).

Perpendicular to both velocity and field. Right-hand rule determines force direction from cross product.

Changes voltage levels in AC circuits. Uses electromagnetic induction to step voltage up or down.

Lenz's Law. Induced current opposes the flux change causing it.

The induced EMF opposes the change in magnetic flux. Conservation of energy principle preventing perpetual motion.

$\tau = \text{n} \times \text{I} \times \text{A} \times \text{B} \times \text{sin}(\theta)$. $n$ is number of turns, $A$ is loop area.

Inducing EMF through changing magnetic flux. Faraday's fundamental discovery linking magnetism and electricity.

Increases induced EMF. Stronger field creates larger flux changes per time.

Weber (Wb). Same as Tesla-meter squared ($\text{T}\cdot\text{m}^2$).

Rate of change of magnetic flux. Faster flux changes produce larger induced EMF.

No magnetic force. Force is zero when velocity parallel to field.

Induced current increases. Lower resistance allows more current for same EMF.

Induced EMF increases. Larger area means more magnetic field lines enclosed.

Ampere (A). Base unit for electric current in SI system.

Determining direction of magnetic force or field. Fingers point along first vector, thumb shows result direction.

EMF induced in a conductor moving in a magnetic field. Moving conductor cuts magnetic field lines inducing EMF.

$\text{EMF} = 3 \text{ V}$. $\text{EMF} = 2 \times 0.5 \times 3 \times \sin(90°) = 3$ V.

$\text{F} = 6 \text{ N}$. $F = qvB\sin(90°) = 1 \times 2 \times 3 = 6$ N.