Author: dexter
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Problem 6.120 — Selection Rules for Electric Dipole: Derivation
Problem Statement Using the matrix element $\langle f|\mathbf{r}|i\rangle$, derive the electric dipole selection rules $\Delta l = \pm1$, $\Delta m_l = 0, \pm1$. 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…
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Irodov Problem 3.18 — Electric Dipole: Far-Field Potential and Field
Problem Statement An electric dipole of moment $p = ql$ is at the origin. Find the potential $\varphi$ and field $E$ at distance $r \gg l$ at angle $\theta$ from the dipole axis. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts…
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Problem 4.227 — Waves: Acoustic Black Holes
Problem Statement Solve the oscillation/wave problem: Solve the oscillation/wave problem: An acoustic black hole is a region where the wave speed $v(x) \to 0$ as $x \to x_0$ (e.g., a tapered plate where $v \propto (x_0-x)^m$). What happens to a wave approaching this point? As $v \to 0$, the wavelength $\lambda = v/f \to 0$…
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Problem 3.351 — Magnetic fields and forces
Problem Statement Solve the magnetic field/force problem: Problem 3.351 — Magnetic fields and forces $c = 3\times10^8\,\text{m/s}$ Newton’s second law $\mathbf{F}_\text{net} = m\mathbf{a}$ is the fundamental relation between net force and acceleration. For systems of connected objects (Atwood machine, blocks on inclines), each body is treated separately wi Given Information Current $I$ or charge $q$…
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HCV Ch26 P10 – Entropy: Heat Transfer Between Two Bodies
Problem Statement Solve the thermodynamics problem: 100 J of heat flows irreversibly from a hot body at 400 K to a cold body at 300 K. Find the total entropy change of the universe. See problem statement for all given quantities. Entropy is a state function measuring the dispersal of energy. The Second Law requires…
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Problem 6.127 — Quantum Confinement: Quantum Dot
Problem Statement Solve the quantum/modern physics problem: Problem 6.127 — Quantum Confinement: Quantum Dot $= \frac{3\times1.047\times10^{-67}}{1.822\times10^{-46}} = 1.72\times10^{-20} \text{ J} = 0.107 \text{ eV}$ $E_{211} = \frac{\pi^2\hbar^2}{2m_eL^2}(4+1+1) = 2E$ This problem applies fundamental physics principles to the scenario described. The soluti Given Information Frequency $\nu$ or wavelength $\lambda$ of radiation Work function $\phi$ of metal…
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Problem 3.350 — Magnetic fields and forces
Problem Statement Solve the magnetic field/force problem: Problem 3.350 — Magnetic fields and forces $c = 3\times10^8\,\text{m/s}$ Newton’s second law $\mathbf{F}_\text{net} = m\mathbf{a}$ is the fundamental relation between net force and acceleration. For systems of connected objects (Atwood machine, blocks on inclines), each body is treated separately wi Given Information Current $I$ or charge $q$…
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HC Verma Chapter 31 Problem 69 – Leakage Current in Capacitor
Problem Statement Solve the capacitor/capacitance problem: A $10\mu$F capacitor has dielectric constant $K = 2.5$ and resistivity $\rho = 10^{12}\,\Omega$ m, thickness 1 mm, area 50 cm$^2$. Find the leakage resistance and the RC time constant. See problem statement for all given quantities. Capacitors store electric charge on conducting plates separated by Given Information Plate…
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Problem 4.226 — Waves: Coupled Mechanical and Acoustic Resonators
Problem Statement Solve the oscillation/wave problem: Problem 4.226 — Waves: Coupled Mechanical and Acoustic Resonators See problem statement for all given quantities. This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving syst Given Information Mass $m$ and spring constant $k$…
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Irodov Problem 3.17 — Work Done Moving a Charge in a Coulomb Field
Problem Statement Solve the work-energy problem: Find the work done by the field of charge $q = 10\,\mu\text{C}$ when test charge $q_0 = 1\,\mu\text{C}$ moves from $r_A = 5\,\text{cm}$ to $r_B = 15\,\text{cm}$. $r_A = 5\,\text{cm}$ $r_B = 15\,\text{cm}$ This problem applies fundamental physics principles to the scenario described. The solution req Given Information Mass…