Category: Part 3: Electricity

Problem Statement Solve the work-energy problem: Irodov Problem 3.36. $$U_{\text{solid}} = \frac{3Q^2}{20\pi\varepsilon_0 R} = \frac{3kQ^2}{5R}$$ (integrate $\varepsilon_0 E^2/2$ over all space). 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…

Problem Statement Solve the magnetic field/force problem: Irodov Problem 3.113. At centre: $B \approx \mu_0 nI$ (same as infinite for $L\gg R$). At end: $B_{\text{end}} = \mu_0 nI/2$ (halved). 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…

Problem Statement Solve the magnetic field/force problem: Irodov Problem 3.152 — Magnetostatics and magnetic forces. Key law: $B_{\text{wire}} = \mu_0 I/(2\pi r)$, torque $\tau = mB\sin\theta$, force $F = qvB\sin\theta$ This problem from the Magnetostatics and magnetic forces section requires applying the governing equation with the given geometry and nume Given Information Current $I$ or…

Problem Statement Irodov Problem 3.69. 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 Irodov Problem 3.33. 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 magnetic field/force problem: Irodov Problem 3.110. $U = -mB\cos\theta$. At $\theta=0°$: $-1\,\text{J}$; $90°$: $0$; $180°$: $+1\,\text{J}$. Work to flip: $2mB = \boxed{2.0\,\text{J}}$. 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…

Problem Statement Irodov Problem 3.67. 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 elasticity problem: Irodov Problem 3.34. $$\nabla^2 V = -\rho/\varepsilon_0\text{ (Poisson)}; \quad \nabla^2 V = 0\text{ (Laplace, charge-free)}$$ Given Information Material’s Young’s modulus $Y$ or Bulk modulus $B$ or Shear modulus $G$ Dimensions (length $L$, area $A$) and applied force or pressure Physical Concepts & Formulas Elasticity quantifies a material’s resistance to…

Problem Statement Solve the magnetic field/force problem: Irodov Problem 3.111. $$B = \frac{\mu_0 Il}{2\pi R\sqrt{R^2+l^2}}$$ Limits: $l\to\infty$ gives infinite wire; $l\ll R$ gives dipole. 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 Analyze the circuit: Irodov Problem 3.68. Diode: $I=I_0(e^{eV/kT}-1)$. At $+0.6\,\text{V}$: $I\approx12\,\text{A}$. At $-0.6\,\text{V}$: $I\approx -I_0 = -1\,\text{nA}$. 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…