PHY 2049 Exam 3 Master Guide: Chapters 25–28

Vocabulary flashcards covering current, resistance, DC circuits, magnetic forces, and sources of magnetic fields based on Chapters 25 through 28 of Young & Freedman's University Physics (13th edition).

Electric Current ($I$)

The rate at which electric charge passes through a cross-section of a conductor, defined as $I = \frac{\Delta Q}{\Delta t}$ (or $I = \frac{dQ}{dt}$), measured in amperes ($\text{A} = \text{C/s}$).

Drift Speed ($v_d$)

The average speed at which charge carriers move through a conductor in response to an electric field, governed by $v_d = \frac{I}{n |q| A}$, where $n$ is carrier density and $A$ is cross-sectional area.

Current Density ($J$)

The current per unit cross-sectional area of a conductor ($J = \frac{I}{A}$), which relates to the internal electric field and resistivity in an Ohmic material via $E = \rho J$.

Resistivity ($\rho$)

An intrinsic material property defined by $\rho = \frac{E}{J}$ that determines the electrical resistance of a uniform conductor of length $L$ and area $A$ through $R = \frac{\rho L}{A}$.

Temperature Coefficient of Resistivity ($\alpha$)

The fractional change in resistance or resistivity per unit temperature change, modeled for metals by $R = R_0[1 + \alpha(T - T_0)]$.

Terminal Voltage ($V_t$)

The actual potential difference across a battery's terminals, given by $V_t = \mathcal{E} - I r$ when discharging and $V_t = \mathcal{E} + I r$ when charging, where $r$ is internal resistance.

Short-Circuit Current ($I_{\text{short}}$)

The idealized current drawn from a real battery when external load resistance is reduced to zero ($R \approx 0\,\Omega$), limited only by internal resistance: $I_{\text{short}} = \frac{\mathcal{E}}{r}$.

Series Resistors

Circuit components connected along a single electrical path that carry identical current and share voltage, with equivalent resistance $R_{\text{eq}} = R_1 + R_2 + \dots$.

Parallel Resistors

Circuit components connected across the same two common nodes that maintain equal potential differences, with equivalent resistance determined by $\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots$.

Kirchhoff's Junction Rule

A statement of charge conservation requiring that the sum of all currents entering a branching node equals the sum of all currents leaving it ($\sum I_{\text{in}} = \sum I_{\text{out}}$).

Kirchhoff's Loop Rule

A statement of energy conservation stating that the algebraic sum of electric potential differences around any closed circuit loop equals zero ($\sum \Delta V = 0$).

Ideal Ammeter

A current-measuring instrument designed with zero internal resistance ($R \approx 0\,\Omega$) that must be connected in series with the component of interest.

Ideal Voltmeter

A potential-measuring instrument designed with infinite internal resistance ($R \rightarrow \infty$) that must be connected in parallel across the component of interest.

Balanced Wheatstone Bridge

A four-resistor bridge circuit where opposite branch resistance ratios are identical ($\frac{R_1}{R_2} = \frac{R_3}{R_4}$), causing equal midpoint potentials and zero bridge current.

RC Time Constant ($\tau$)

The characteristic time scale for an RC circuit given by $\tau = R C$, marking the elapsed time at which a charging capacitor gains approximately $63.2\%$ of its final potential difference.

Steady-State DC Capacitor Behavior

The operational state reached after a long time ($t \rightarrow \infty$) in a DC circuit where charging current falls to zero ($I \rightarrow 0\,\text{A}$) and the capacitor acts as an open circuit holding maximum voltage ($V_C = \mathcal{E}$).

Magnetic Force on a Moving Charge

The sideways force on a charge $q$ moving with velocity $\mathbf{v}$ in a magnetic field $\mathbf{B}$, given by $\mathbf{F} = q(\mathbf{v} \times \mathbf{B})$ with magnitude $F = |q|vB\sin(\theta)$.

Work Done by a Static Magnetic Field

The mechanical work performed on a moving charged particle by a magnetic force, which is strictly zero ($W = 0$) because $\mathbf{F} \perp \mathbf{v}$, leaving speed and kinetic energy unaltered.

Cyclotron Radius ($r$)

The orbital radius of a charged particle executing circular motion perpendicular to a uniform magnetic field, derived from centripetal force balance as $r = \frac{m v}{|q| B}$.

Cyclotron Period ($T$)

The time required for a charged particle to complete one circular revolution in a magnetic field, given nonrelativistically by $T = \frac{2\pi m}{|q| B}$, which is independent of particle speed.

Velocity Selector

An arrangement of perpendicular electric and magnetic fields where electric and magnetic forces balance ($|q|E = |q|vB$), allowing only particles with speed $v = \frac{E}{B}$ to pass undeflected.

Magnetic Dipole Moment ($\mu$)

A vector characteristic of a current loop of $N$ turns and area $A$ carrying current $I$, with magnitude $\mu = N I A$, which experiences a torque $\boldsymbol{\tau} = \boldsymbol{\mu} \times \mathbf{B}$ in an external field.

Magnetic Flux ($\Phi_B$)

The measure of total magnetic field passing through an area, defined as $\Phi_B = B A \cos(\theta)$, where $\theta$ is measured relative to the surface normal vector.

Gauss's Law for Magnetism

The electromagnetic principle stating that the net magnetic flux through any closed surface is identically zero ($\oint \mathbf{B} \cdot d\mathbf{A} = 0$), reflecting the nonexistence of magnetic monopoles.

Hall Effect

The generation of a transverse potential difference ($|V_H| = \frac{I B}{n |q| t}$) across a conductor of thickness $t$ carrying current $I$ in a perpendicular magnetic field $B$, caused by carrier deflection.

Motor Back EMF ($\mathcal{E}_{\text{back}}$)

The counter-electromotive force generated by the rotation of an electric motor's coil that opposes the supplied terminal voltage, governed by $V = \mathcal{E}_{\text{back}} + I r$.

Biot–Savart Law

The fundamental relationship defining the magnetic field contribution $d\mathbf{B}$ produced by an infinitesimal current element $I d\mathbf{l}$, with magnitude $dB = \left(\frac{\mu_0}{4\pi}\right) \frac{I\,dl\sin(\theta)}{r^2}$.

Ampere's Law

The magnetostatic law stating that the line integral of magnetic field around any closed loop equals the permeability constant times the net enclosed current: $\oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 I_{\text{enclosed}}$.

Long Straight Wire Magnetic Field

The concentric magnetic field lines created by a current $I$ at perpendicular distance $r$, given by $B = \frac{\mu_0 I}{2\pi r}$, decreasing inversely with distance ($B \propto \frac{1}{r}$).

Parallel-Wire Magnetic Force

The mutual interaction between two long straight parallel conductors carrying currents $I_1$ and $I_2$, with force per unit length $\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi r}$; currents in the same direction attract, while opposite currents repel.

Ideal Solenoid Interior Field

The nearly uniform magnetic field inside a closely wound, long helical coil with $n$ turns per unit length carrying current $I$, modeled by $B = \mu_0 n I$.

Toroid Magnetic Field

The circular magnetic field confined within the winding region of a donut-shaped coil with $N$ turns at distance $r$ from the central axis: $B = \frac{\mu_0 N I}{2\pi r}$.

Magnetic Susceptibility ($\chi_m$)

A dimensionless parameter relating relative permeability via $\chi_m = K_m - 1$, which is small and positive for paramagnetic materials and small and negative for diamagnetic materials.