Category: Part 3: Electricity

Problem Statement Solve the magnetic field/force problem: Irodov Problem 3.127. Along axis: $F = -3\mu_0 m^2/(2\pi r^4)$ — attractive for aligned dipoles. 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…

Problem Statement Solve the magnetic field/force problem: Irodov Problem 3.262 — 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 3.162 — 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 work-energy problem: Irodov Problem 3.79. At 220 kV: $I=454\,\text{A}$, loss $= I^2\times20\,\Omega = 4.1\,\text{MW}$, efficiency 96%. At 11 kV: loss $> P_{\text{total}}$! 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…

Problem Statement Solve the capacitor/capacitance problem: Irodov Problem 3.47. Series (perpendicular to $E$): $C = \varepsilon_0 A/(d_1/\varepsilon_1+d_2/\varepsilon_2)$. $D$ is the same in both layers; $E$ is different. 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…

Problem Statement Solve the magnetic field/force problem: Irodov Problem 3.124. $$u = \frac{B^2}{2\mu_0},\quad U = \frac{1}{2}LI^2$$ For solenoid: both expressions agree, confirming $u = B^2/(2\mu_0)$. 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 3.259 — 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 3.163 — 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 3.80. 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 3.48. Battery connected: $V$ fixed, $Q$ increases by $\varepsilon_r$, $E$ unchanged, $U$ increases by $\varepsilon_r$. Battery supplies extra energy. 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…