Category: Part 3: Electricity

Problem Statement Irodov Problem 3.98. 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 3.181 — Electromagnetic induction: Faraday’s law. Key law: $\mathcal{E} = -N\,d\Phi/dt$, Lenz’s law, motional EMF $= Blv$ This problem from the Electromagnetic induction: Faraday’s law section requires applying the governing equation with the given geometry and numerical parameters. T Given Information Current $I$ or charge $q$…

Problem Statement Solve the magnetic field/force problem: Irodov Problem 3.143. Adiabatic invariant $\mu_m = mv_\perp^2/(2B)$ = constant. Reflection when $v_\parallel = 0$. Loss cone: $\sin^2\alpha_0 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 magnetic field/force problem: Irodov Problem 3.278 — Electromagnetic induction. This problem belongs to the section on Electromagnetic induction . Key principles: Faraday: $\mathcal{E} = -d\Phi/dt$; Lenz; motional EMF; inductance The solution proceeds by identifying the relevant physical configuration, applying the governing law Given Information Current $I$ or charge $q$ and velocity…

Problem Statement Analyze the circuit: Irodov Problem 3.96. $$R = \frac{\rho}{2\pi l}\ln\frac{b}{a}$$ Note: $RC = \rho\varepsilon_0$ (dielectric relaxation time) for any geometry. 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…

Problem Statement Solve the magnetic field/force problem: Irodov Problem 3.179 — 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 Solve the magnetic field/force problem: Irodov Problem 3.141. $\mathbf{A} = \frac{\mu_0}{4\pi}\frac{\mathbf{m}\times\hat{r}}{r^2}$ for dipole. $\mathbf{B} = \nabla\times\mathbf{A}$ gives dipole field. 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 & Formulas Magnetic fields…

Problem Statement Solve the magnetic field/force problem: Irodov Problem 3.276 — Electromagnetic induction. This problem belongs to the section on Electromagnetic induction . Key principles: Faraday: $\mathcal{E} = -d\Phi/dt$; Lenz; motional EMF; inductance The solution proceeds by identifying the relevant physical configuration, applying the governing law Given Information Current $I$ or charge $q$ and velocity…

Problem Statement Solve the magnetic field/force problem: Irodov Problem 3.97. $m = evr/2 = \boxed{9.3\times10^{-24}\,\text{A}\cdot\text{m}^2}$ for hydrogen ground state = 1 Bohr magneton. 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 & Formulas…

Problem Statement Irodov Problem 3.94. 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…