Category: Part 3: Electricity

Problem Statement Irodov Problem 3.26. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical principles. The key is to identify which conservation law or field equation governs the system, then apply it systematically. Dimensional…

Problem Statement Solve the capacitor/capacitance problem: Irodov Problem 3.60. $V_C(t) = \mathcal{E}(1-e^{-t/RC})$, $I(t) = (\mathcal{E}/R)e^{-t/RC}$. Energy: half from battery is dissipated — independent of $R$! Given Information Plate area $A$ (for parallel plate) or geometry as given Separation $d$ or radii as given Dielectric constant $\kappa$ (if applicable, else $\kappa=1$ for vacuum) Permittivity $\varepsilon_0 =…

Problem Statement Solve the Newton’s Laws / mechanics problem: Irodov Problem 3.104. $$F/L = \frac{\mu_0 I_1 I_2}{2\pi d} = \frac{4\pi\times10^{-7}\times200}{2\pi\times0.01} = \boxed{4\,\text{mN/m}}$$ Parallel currents attract. Given Information Mass(es), forces, angles, and coefficients of friction as given $g = 9.8\,\text{m/s}^2$ (acceleration due to gravity) Physical Concepts & Formulas Newton’s three laws form the complete foundation of…

Problem Statement Analyze the circuit: Irodov Problem 3.57. Balance: $PS = QR$. $R = S\cdot P/Q = 150\times100/300 = \boxed{50\,\Omega}$. Given Information Resistance values $R_1, R_2, \ldots$ as specified EMF $\mathcal{E}$ and internal resistance $r$ of battery Any additional circuit elements given Physical Concepts & Formulas Ohm’s Law $V = IR$ and Kirchhoff’s two laws…

Problem Statement Solve the magnetic field/force problem: Irodov Problem 3.101. Biot-Savart integration: $$B = \frac{\mu_0 I}{2\pi R}$$ Circular field lines around wire (right-hand rule). Given Information Current $I$ or charge $q$ and velocity $v$ as given Geometry (straight wire, loop, solenoid) as specified Permeability of free space $\mu_0 = 4\pi\times10^{-7}\,\text{T m A}^{-1}$ Physical Concepts &…

Problem Statement Irodov Problem 3.24. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical principles. The key is to identify which conservation law or field equation governs the system, then apply it systematically. Dimensional…

Problem Statement Analyze the circuit: Irodov Problem 3.58. Two measurements: $I_1=2\,A$ at $R_1=4\,\Omega$; $I_2=1\,A$ at $R_2=9\,\Omega$. Gives $\boxed{r=1\,\Omega}$, $\boxed{\mathcal{E}=10\,\text{V}}$. Given Information Resistance values $R_1, R_2, \ldots$ as specified EMF $\mathcal{E}$ and internal resistance $r$ of battery Any additional circuit elements given Physical Concepts & Formulas Ohm’s Law $V = IR$ and Kirchhoff’s two laws are…

Problem Statement Solve the magnetic field/force problem: Irodov Problem 3.102. Rectangular loop gives $Bl = \mu_0 nIl$. $$\boxed{B = \mu_0 nI}$$ (inside). $B=0$ outside. Given Information Current $I$ or charge $q$ and velocity $v$ as given Geometry (straight wire, loop, solenoid) as specified Permeability of free space $\mu_0 = 4\pi\times10^{-7}\,\text{T m A}^{-1}$ Physical Concepts &…

Problem Statement Solve the capacitor/capacitance problem: Irodov Problem 3.21. Disconnected: $Q$ constant. $C = \varepsilon_r C_0$, $V = V_0/\varepsilon_r$, $U = U_0/\varepsilon_r$. Energy decrease = work done pulling dielectric in. Given Information Plate area $A$ (for parallel plate) or geometry as given Separation $d$ or radii as given Dielectric constant $\kappa$ (if applicable, else $\kappa=1$…

Problem Statement Analyze the circuit: Irodov Problem 3.55. KVL: $\sum \mathcal{E} = \sum IR$. Series circuit: $I = \mathcal{E}/(R+r) = 12/3 = \boxed{4\,\text{A}}$. $V_t = 12-4\times0.5 = 10\,\text{V}$. Given Information Resistance values $R_1, R_2, \ldots$ as specified EMF $\mathcal{E}$ and internal resistance $r$ of battery Any additional circuit elements given Physical Concepts & Formulas Ohm’s…