Author: dexter
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Irodov Problem 3.87 — Electric Stress Tensor at Interface
Problem Statement Solve the elasticity problem: Solve the elasticity problem: Irodov Problem 3.87 (Section 3.1: Constant Electric Field in Vacuum): This problem applies the fundamental laws of electrostatics to a specific charge configuration involving electric stress tensor at interface. Charge parameters and geometry as specified in Irodov 3.87 Given Information See problem statement for all…
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Problem 2.157 — Thermal Noise: Johnson-Nyquist
Problem Statement A resistor $R=1\ \text{k}\Omega$ is at $T=300\ \text{K}$. Find the rms thermal voltage noise in a bandwidth $\Delta f=10\ \text{kHz}$. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations…
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HCV Ch28 P2 – Heat Conduction: Thermal Resistance and Series Combination
Problem Statement Analyze the circuit: Analyze the circuit: Two rods, one of copper ($k_1 = 400$ W/m·K, $L_1 = 0.1$ m) and one of steel ($k_2 = 50$ W/m·K, $L_2 = 0.2$ m), each of area $A = 10^{-4}$ m² are joined in series. The free ends are at 100°C and 0°C. Find the rate…
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HC Verma Chapter 7 Problem 35 — Period of rotating body from angular acceleration
Problem Statement Solve the kinematics problem: Solve the kinematics problem: A rotor starts from rest and reaches 300 rpm in 1 minute. Find the angular acceleration and the number of revolutions made. $\omega_f = 300 \times 2\pi/60 = 10\pi$ rad/s; $\alpha = \omega_f/t$; $N = \theta/(2\pi)$ Step 1: $\alpha = 10\pi/60 = \pi/6$ rad/s². Step…
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Problem 2.156 — Entropy and Disorder: Rubber Band
Problem Statement Solve the thermodynamics problem: Solve the thermodynamics problem: A rubber band warms when stretched adiabatically. Explain this using thermodynamics and the statistical view of entropy. Statistical: Unstretched rubber has polymer chains in high-entropy random coil configurations ($\Omega$ large). Stretching aligns the chains, red Given Information See problem statement for all given quantities. Physical…
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Irodov Problem 3.86 — Refraction of Field Lines at Interface
Problem Statement Solve the optics problem: Solve the optics problem: Irodov Problem 3.86 (Section 3.1: Constant Electric Field in Vacuum): This problem applies the fundamental laws of electrostatics to a specific charge configuration involving refraction of field lines at interface. Charge parameters and geometry as specified in Irodov 3.86 Given Information See problem statement for…
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Irodov Problem 3.86 — Refraction of Field Lines at Interface
Problem Statement Solve the optics problem: Solve the optics problem: Irodov Problem 3.86 (Section 3.1: Constant Electric Field in Vacuum): This problem applies the fundamental laws of electrostatics to a specific charge configuration involving refraction of field lines at interface. Charge parameters and geometry as specified in Irodov 3.86 Given Information See problem statement for…
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HC Verma Chapter 7 Problem 34 — Maximum Speed on Banked Road with Friction
Problem Statement A circular road is banked at an angle of $ heta = 20°$ and has a radius $r = 100\ ext{m}$. The coefficient of static friction between the tyres and the road is $\mu_s = 0.4$. Find the maximum safe speed for a vehicle on this road. (Take $g = 10\ ext{m/s}^2$, $…
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Problem 2.155 — Adiabatic Demagnetisation
Problem Statement Solve the thermodynamics problem: Solve the thermodynamics problem: Show that adiabatic demagnetisation cools a paramagnet. If $M = CH/T$ (Curie law) and the lattice heat capacity is $C_{lat}$, find the temperature drop when $H$ is reduced from $H_1$ to $H_2$. The entropy of an ideal paramagnet: $S_{mag} = f(H/T)$ (function of $H/T$ Given…
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HCV Ch28 P1 – Heat Conduction: Fourier’s Law
Problem Statement Solve the thermodynamics problem: Solve the thermodynamics problem: A steel rod (thermal conductivity $k = 50$ W/m·K, length $L = 0.5$ m, cross-sectional area $A = 2 \times 10^{-4}$ m²) has its two ends at 100°C and 0°C. Find the rate of heat flow through the rod in steady state. $k = 50$…