Category: Part 3: Electricity

Problem Statement Analyze the circuit: Irodov Problem 3.65. $\sigma = j/E$; $v_d = j/(ne)$; $\mu = v_d/E = \sigma/(ne)$. For copper: $v_d \approx 0.37\,\text{mm/s}$ at $j=5\times10^6\,\text{A/m}^2$. 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…

Problem Statement Determine the electric field for the configuration described: Irodov Problem 3.32. Vector sum contributions from each charge. Example: two charges give total field by component addition. Given Information Geometry and charge distribution as given in the problem Permittivity of free space $\varepsilon_0 = 8.85\times10^{-12}\,\text{C}^2\text{N}^{-1}\text{m}^{-2}$ Coulomb constant $k = 1/(4\pi\varepsilon_0) = 9\times10^9\,\text{N m}^2\text{C}^{-2}$ Physical…

Problem Statement Analyze the circuit: Irodov Problem 3.109. $\tau = mB\sin\alpha = IAB\sin\alpha$. For 30° loop angle, $\alpha = 60°$: $\tau = 0.012\times0.8\times\sin60° = \boxed{8.3\,\text{mN}\cdot\text{m}}$. 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 =…

Problem Statement Solve the magnetic field/force problem: Irodov Problem 3.66. $V_H = IB/(nte)$ where $t$ is thickness. For copper strip at $B=1.5\,\text{T}$, $I=100\,\text{A}$: $V_H \approx 5.5\,\mu\text{V}$ (tiny, as $n$ is large). 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…

Problem Statement Irodov Problem 3.29. 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 3.63. Two batteries with shared external $R$: apply KCL + KVL to get system of equations. One battery may be charging. 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…

Problem Statement Solve the work-energy problem: Irodov Problem 3.30. For equilateral triangle (side $a$): $$U = \frac{q_1q_2+q_1q_3+q_2q_3}{4\pi\varepsilon_0 a}$$ Given Information Mass $m$, velocity $v$, height $h$, or other given quantities Any forces doing work (conservative or non-conservative) as specified Physical Concepts & Formulas The Work-Energy Theorem states that the net work done on an object…

Problem Statement Solve the magnetic field/force problem: Irodov Problem 3.107. $r = m_p v/(eB) = 4.2\,\text{cm}$. Cyclotron frequency: $f_c = eB/(2\pi m_p) = 7.6\,\text{MHz}$ — independent of speed! 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…

Problem Statement Solve the thermodynamics problem: Irodov Problem 3.64. $P = I^2 R = VI = V^2/R$. Heater 220 V, 10 A: $R=22\,\Omega$, $P=2200\,\text{W}$. In 30 min: $Q=3.96\,\text{MJ} = 946\,\text{kcal}$. Given Information Temperatures, pressures, volumes, and process type as given Universal gas constant $R = 8.314\,\text{J mol}^{-1}\text{K}^{-1}$ $C_p$ and $C_v$ or $\gamma = C_p/C_v$ as…

Problem Statement Solve the Newton’s Laws / mechanics problem: Irodov Problem 3.31. Two charges $3\,\mu$C each, 50 cm apart: $F = 0.32\,\text{N}$ (repulsive). Field at midpoint = 0 by symmetry. 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…