Author: dexter
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Problem 4.229 — Waves: Acoustic Analogue of Electromagnetics
Problem Statement Solve the magnetic field/force problem: Solve the magnetic field/force problem: Write the complete acoustic equations in a form analogous to Maxwell’s equations, identifying the acoustic equivalents of $\mathbf{E}$, $\mathbf{H}$, $\epsilon$, and $\mu$. The linearized acoustic equations are: $$\rho\frac{\partial\mathbf{v}}{\partial t} = -\ Given Information Current $I$ or charge $q$ and velocity $v$ as given…
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Problem 6.121 — Hydrogen Stark Effect
Problem Statement For the $n=2$ states of hydrogen in an electric field $\mathcal{E}$, find the first-order energy shifts (linear Stark effect). 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…
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Irodov Problem 3.19 — Dipole in a Uniform External Field: Torque and Energy
Problem Statement Solve the rotational mechanics problem: Solve the work-energy problem: Find the torque on a dipole $\vec{p}$ in uniform field $\vec{E}$, the potential energy, and equilibrium stability. $\vec{p}$ = dipole moment, $\vec{E}$ = uniform field, $\theta$ = angle between them Net force is zero (uniform field). Torque aligns the dipole with the f Given…
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Problem 3.353 — Magnetic fields and forces
Problem Statement Solve the magnetic field/force problem: Solve the magnetic field/force problem: Irodov Problem 3.353 — Magnetic fields and forces. This problem belongs to the section on Magnetic fields and forces . Key principles: Biot-Savart, Ampere, force on current, magnetic materials The solution proceeds by identifying the relevant physical configur Given Information Current $I$ or…
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HCV Ch26 P11 – Thermodynamic Cycles: PV Diagram Work Calculation
Problem Statement Solve the thermodynamics problem: Solve the work-energy problem: An ideal gas undergoes a cycle: A→B isothermal at 400 K from $V=1$ L to $V=4$ L; B→C isochoric cooling to 300 K; C→A isothermal at 300 K from $V=4$ L to $V=1$ L. Find net work done per cycle. $n = 1$ mol, $T_{AB}…
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Problem 4.228 — Waves: Acoustic Self-Collimation in Phononic Crystals
Problem Statement Solve the oscillation/wave problem: Solve the oscillation/wave problem: In a phononic crystal with a flat equifrequency contour (EFC), acoustic waves can propagate without diffraction spreading (self-collimation). Explain the condition and estimate the collimation frequency for a crystal with lattice constant $a = 1$ mm. Self-collimat Given Information Mass $m$ and spring constant $k$…
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Problem 6.128 — Born Approximation: Scattering Cross Section
Problem Statement Using the Born approximation, find the differential scattering cross section for a Yukawa potential $V = (V_0/r)e^{-r/a}$. 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…
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HC Verma Chapter 31 Problem 70 – Capacitance Between Two Spheres
Problem Statement Solve the capacitor/capacitance problem: Solve the capacitor/capacitance problem: Derive the capacitance of a spherical capacitor and then find it for inner radius 10 cm, outer radius 15 cm. Derivation: Field between spheres: $E = kQ/r^2$. Potential difference: $$V = \int_a^b \frac{kQ}{r^2}dr = kQ\left(\frac{1}{a}-\frac{1}{b}\right)$$ $$C Given Information Plate area $A$ (for parallel plate) or…
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Problem 3.352 — Magnetic fields and forces
Problem Statement Solve the magnetic field/force problem: Solve the magnetic field/force problem: Irodov Problem 3.352 — Magnetic fields and forces. This problem belongs to the section on Magnetic fields and forces . Key principles: Biot-Savart, Ampere, force on current, magnetic materials The solution proceeds by identifying the relevant physical configur Given Information Current $I$ or…
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Problem 6.184 — Radioactive Decay: Multiple Branches
Problem Statement Solve the nuclear physics problem: Solve the nuclear physics problem: A nucleus can decay by alpha ($\lambda_\alpha$) or beta ($\lambda_\beta$) emission. Find the total half-life and the branching fractions. When multiple decay channels are available, the total decay constant is the sum: $$\lambda_{total} = \lambda_\alpha + \lambda_\ Given Information Nuclide symbol, atomic number…