Category: Part 3: Electricity

Problem Statement Solve the magnetic field/force problem: Irodov Problem 3.177 — 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 3.139. $\mathbf{B} = \mu_0 g/(4\pi r^2)\hat{r}$. Current physics: $\nabla\cdot\mathbf{B}=0$ — no monopoles. Dirac: $eg/\hbar c = n/2$ would explain charge quantization. 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 Solve the magnetic field/force problem: Irodov Problem 3.274 — 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 3.95. $$R = \frac{\rho}{4\pi}\left(\frac{1}{a}-\frac{1}{b}\right)$$ As $b\to\infty$: spreading resistance $= \rho/(4\pi a)$. 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 the…

Problem Statement Solve the magnetic field/force problem: Irodov Problem 3.178 — 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 3.140. $\mathbf{B} = \nabla\times\mathbf{A}$, always valid since $\nabla\cdot\mathbf{B}=0$. For infinite wire: $A_z = -\mu_0 I\ln r/(2\pi)$. 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 3.275 — 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 3.137. $$\mathbf{g} = \varepsilon_0(\mathbf{E}\times\mathbf{B}) = \mathbf{S}/c^2$$ Static charge near magnetic dipole carries field momentum — explains recoil when current is cut. 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 Solve the magnetic field/force problem: Irodov Problem 3.272 — 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 Irodov Problem 3.93. 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…