Category: Part 3: Electricity

Problem Statement Analyze the circuit: Irodov Problem 3.52. $R = \rho l/A = 1.7\times10^{-8}\times100/(7.85\times10^{-7}) = \boxed{2.17\,\Omega}$. At 2.5 A: $V = IR = \boxed{5.4\,\text{V}}$. 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 $V = IR$…

Problem Statement Two point charges $+q$ and $-q$ are separated by distance $2a$. Describe the equipotential surfaces and find the potential at the midpoint. Given Information Charge $+q$ at position $(-a, 0)$ Charge $-q$ at position $(+a, 0)$ Separation $d = 2a$ Physical Concepts & Formulas An equipotential surface is a locus of all points…

Problem Statement Solve the capacitor/capacitance problem: Irodov Problem 3.16. $$\boxed{C = \frac{\varepsilon_r\varepsilon_0 A}{d}}$$ With $\varepsilon_r=1$, $A=0.01\,\text{m}^2$, $d=1\,\text{mm}$: $C = 88.5\,\text{pF}$. 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 $\varepsilon_0 = 8.85\times10^{-12}\,\text{F m}^{-1}$ Physical Concepts &…

Problem Statement Irodov Problem 3.13. 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 3.14. 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 3.11. 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 work-energy problem: Irodov Problem 3.12. Work by field: $W = q(V_A – V_B)$. From 200 V to 800 V for $q = 1\,\mu$C: $W = -0.60\,\text{mJ}$ (field opposes motion uphill in potential). Given Information Mass $m$, velocity $v$, height $h$, or other given quantities Any forces doing work (conservative or non-conservative)…

Problem Statement An infinitely long cylinder of radius $R$ carries surface charge $\sigma$. Find $E$ inside and outside. 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…

Problem Statement A solid cylinder of radius $R$ has volume charge density $\rho$. Find $E$ at distance $r$. 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…

Problem Statement Determine the electric field for the configuration described: An infinite plane has surface charge density $\sigma$. Find the electric field. Pillbox Gaussian surface straddles the plane. Flux through two flat faces = $2EA$. Enclosed charge = $\sigma A$. $$\boxed{E = \frac{\sigma}{2\varepsilon_0}}$$ Field is uniform and independent of distance from the plane. Given Information…