Physics Test 2 Review: Electromagnetism, Circuits, and Potentials

Vocabulary practice flashcards covering formulas, definitions, and principles from chapters 25 through 29, including electric potential, capacitance, circuits, Kirchhoff's rules, and magnetic fields.

Electrical Current ($I$)

The rate of flow of electric charge over time, given by $I = \frac{\Delta Q}{\Delta t}$, measured in amperes ($[\text{Ampere}]$ or $[\text{A}]$).

Ohm's Law

An empirical law relating voltage, current, and resistance in a circuit: $V = I R$.

Electrical Resistance ($R$)

The opposition to current flow defined by $R = \frac{V}{I} = \left[\frac{\text{V}}{\text{A}}\right] = [\text{ohms}] = \Omega$, which is directly proportional to length ($R \propto l$) and inversely proportional to cross-sectional area ($R \propto \frac{1}{A}$).

Electric Power ($P$)

The rate at which electrical energy is transferred or work is performed, given by $\text{Power} = \frac{\text{Work}}{\text{Time}} = \frac{\text{Energy}}{\text{Time}} = \left[\frac{\text{Joule}}{\text{sec}}\right] = [\text{Watts}]$.

Current Density ($J$)

The measure of electrical current flowing per unit of cross-sectional area, expressed as $J = \frac{I}{A}$.

Kirchhoff's Junction Rule

The conservation law stating that the total current entering a junction equals the total current leaving the junction: $\sum I_{\text{in}} = \sum I_{\text{out}}$.

Kirchhoff's Loop Rule

The conservation law stating that the sum of the potential differences (voltages) around any closed circuit loop is zero: $\sum V_i = 0$.

RC Time Constant ($\tau$)

The characteristic time required for charging or discharging a capacitor through a resistor, calculated as $\tau = R C$.

Capacitor Charging Equations

The mathematical functions describing an $RC$ charging circuit over time: voltage $V(t) = V_0 (1 - e^{-t/RC})$, current $I(t) = \frac{V_0}{R} e^{-t/RC}$, and charge $Q(t) = C V_0 (1 - e^{-t/RC})$.

Capacitor Discharging Equations

The mathematical functions describing an $RC$ discharging circuit over time: voltage $V(t) = V_0 e^{-t/RC}$, current $I(t) = -\frac{V_0}{R} e^{-t/RC}$, and charge $Q(t) = C V_0 e^{-t/RC}$.

Magnetic Force on a Moving Charge

The deflecting force exerted on a moving charge $q$ by a magnetic field $\mathbf{B}$, given in vector form by $\mathbf{F} = q \mathbf{v} \times \mathbf{B}$ and in scalar form by $F = q v B \sin(\theta)$.

Magnetic Force on a Current-Carrying Wire

The force exerted on a wire of length vector $\mathbf{L}$ conducting current $I$ in a magnetic field $\mathbf{B}$, given by $\mathbf{F} = I \mathbf{L} \times \mathbf{B}$ and $F = I L B \sin(\theta)$.

Biot-Savart Law

The fundamental law for the magnetic field produced by a moving point charge, expressed in scalar form as $B = \frac{\mu_0}{4\pi} \frac{q v \sin(\theta)}{r^2}$ and in vector form as $\mathbf{B} = \frac{\mu_0}{4\pi} \frac{q \mathbf{v} \times \hat{r}}{r^2}$.

Bound Orbit vs. Unbound Orbit Condition

The energetic criterion determining orbital states: an orbit is bound when potential energy exceeds kinetic energy ($U > K$), and unbound (escape) when kinetic energy exceeds potential energy ($K > U$).

Electrostatic Escape Velocity ($v_{\text{esc}}$)

The initial speed needed for a charged particle of mass $m$ to escape the electric potential of another charge: $v = \sqrt{\frac{2 k q_1 q_2}{m r}}$.

Electric Potential ($V$)

The electrostatic potential energy per unit charge ($V = \frac{U}{q}$), which for a point charge evaluates to $V = \frac{k q}{r}$.

Potential Gradient Relation

The spatial derivative relationship between electric field and potential: $E = -\frac{dV}{ds}$, where the negative sign denotes that the electric field points in the direction of decreasing potential.

Capacitance ($C$)

The ability of a system to store electric charge per unit potential difference, defined as $C = \frac{Q}{V}$, with units of farads ($\left[\frac{\text{C}}{\text{V}}\right] = \text{Farad}$).

Parallel Plate Capacitor (PPC)

A configuration of two parallel conducting plates of area $A$ separated by distance $d$, having capacitance $C = \frac{\varepsilon_0 A}{d}$ and electric field $E = \frac{\sigma}{\varepsilon_0} = \frac{Q}{\varepsilon_0 A}$.

Energy Stored in a Capacitor ($U$)

The electric potential energy held in the electric field of a charged capacitor, given by $U = \frac{1}{2} \frac{Q^2}{C} = \frac{1}{2} C V^2 = \frac{1}{2} Q V$.

Dielectric Effect

The phenomenon where inserting a dielectric material weakens the electric field ($E_{\text{net}} = E_0 - E_{\text{induced}}$) while increasing capacitance ($C = \kappa C_0$) and decreasing stored energy ($U = \frac{1}{\kappa} U_0$) when isolated at constant charge.

Electron Drift Current

The electric current expressed in terms of charge carrier density $n$, cross-sectional area $A$, elementary charge $e$, and drift velocity $v_d$, given by $I = n A e v_d$.