Create PHY_613_Electromagnetic_Theory_II.py

pages/PHY_613_Electromagnetic_Theory_II.py

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+import streamlit as st
+
+# Set the page title
+st.title("PHY 613: Electromagnetic Theory II")
+
+# Course Details
+st.markdown("""
+## Course Details
+- **Course Title**: Electromagnetic Theory II  
+- **Credits**: 3  
+- **Prerequisites**: PHY 611  
+- **Instructor**: [Instructor Name]  
+- **Office Hours**: [Office Hours]  
+
+## Course Description
+This course builds upon Electromagnetic Theory I and focuses on advanced topics in electromagnetism, including electromagnetic wave propagation, optical phenomena, radiation theory, and the covariant formulation of Maxwell’s equations.
+
+## Course Objectives
+By the end of this course, students will:
+- Be proficient in the theory of electromagnetic waves.
+- Understand the interaction of electromagnetic radiation with matter.
+- Apply the covariant formulation of Maxwell’s equations to physical problems.
+
+---
+""")
+
+# Weekly Outline with Problems
+
+# Week 1: Review of Maxwell’s Equations
+with st.expander("**Week 1: Review of Maxwell’s Equations**"):
+    st.markdown("""
+    ### Topics Covered
+    - Maxwell’s Equations: Review of integral and differential forms of Maxwell’s equations in free space and in materials.
+    - Energy and Momentum Conservation: Derivation and applications of the Poynting theorem.
+    - Boundary Conditions: Conditions on electric and magnetic fields at material interfaces.
+    
+    ### Problems
+    1. Derive Maxwell’s equations in a vacuum from the differential forms of Gauss’s law and Ampère’s law with displacement current.
+    2. Solve for the electric and magnetic fields in a region with a time-varying current distribution.
+    3. Calculate the energy stored in the electric field of a spherical charge distribution.
+    4. Derive the Poynting vector from Maxwell’s equations and compute the energy flux through a closed surface.
+    5. Apply Maxwell’s equations to solve for the fields around a current loop in free space.
+    6. Solve for the boundary conditions of the electric and magnetic fields at the interface between two dielectrics.
+    """)
+
+# Week 2-3: Electromagnetic Wave Propagation
+with st.expander("**Week 2-3: Electromagnetic Wave Propagation: Polarization, Dispersion**"):
+    st.markdown("""
+    ### Topics Covered
+    - Wave Equation: Derivation of the electromagnetic wave equation from Maxwell’s equations.
+    - Polarization: Linear, circular, and elliptical polarization; manipulation of polarized waves.
+    - Dispersion: Understanding phase velocity, group velocity, and wave dispersion in different media.
+
+    ### Problems
+    7. Derive the wave equation for an electromagnetic field in a dielectric medium.
+    8. Solve for the electric and magnetic fields of a plane wave propagating through free space.
+    9. Analyze the polarization state of an electromagnetic wave passing through a birefringent medium.
+    10. Derive the dispersion relation for electromagnetic waves in a plasma.
+    11. Calculate the group and phase velocities for an electromagnetic wave propagating in a dispersive medium.
+    12. Solve for the reflection and transmission coefficients of an electromagnetic wave incident on a dielectric boundary.
+    13. Calculate the power carried by an electromagnetic wave in a vacuum using the Poynting vector.
+    14. Determine the behavior of circularly polarized light when passing through an optically active medium.
+    15. Analyze the propagation of an electromagnetic wave in a conductor and calculate the skin depth.
+    16. Solve for the electromagnetic fields of a plane wave propagating through a conducting medium.
+    """)
+
+# Week 4-5: Waveguides and Resonant Cavities
+with st.expander("**Week 4-5: Waveguides and Resonant Cavities**"):
+    st.markdown("""
+    ### Topics Covered
+    - Waveguides: TE (transverse electric), TM (transverse magnetic), and TEM (transverse electromagnetic) modes in waveguides.
+    - Resonant Cavities: Modes, eigenfrequencies, and boundary conditions in resonant cavities.
+    - Energy Storage and Loss: Quality factor of cavities and waveguides.
+
+    ### Problems
+    17. Derive the TE and TM modes of a rectangular waveguide and calculate the cutoff frequency.
+    18. Solve for the electromagnetic fields in a cylindrical waveguide and determine the modes that propagate.
+    19. Calculate the resonant frequencies for a rectangular cavity and analyze the boundary conditions.
+    20. Derive the quality factor for a resonant cavity with conducting walls.
+    21. Solve for the wave impedance in a rectangular waveguide operating in the TE mode.
+    22. Calculate the power transmitted through a waveguide as a function of the mode and frequency.
+    23. Solve for the fields inside a resonant cavity with mixed boundary conditions.
+    24. Analyze the energy stored in a resonant cavity and calculate the energy loss due to imperfect conductors.
+    25. Derive the expression for the cutoff wavelength in a rectangular waveguide.
+    26. Compute the electromagnetic field distribution inside a cavity operating in the TM mode.
+    """)
+
+# Week 6: Optical Phenomena
+with st.expander("**Week 6: Optical Phenomena: Interference, Diffraction, and Polarization**"):
+    st.markdown("""
+    ### Topics Covered
+    - Interference: Understanding interference of light waves; examples include Young’s double-slit experiment.
+    - Diffraction: Fraunhofer and Fresnel diffraction; diffraction patterns from apertures and obstacles.
+    - Polarization: The use of polarizers, birefringence, and optical rotation.
+
+    ### Problems
+    27. Derive the interference pattern for a double-slit experiment with coherent light sources.
+    28. Solve for the diffraction pattern of light passing through a single slit using Fraunhofer diffraction.
+    29. Calculate the intensity of light after passing through a polarizer and an analyzer at different angles.
+    30. Analyze the interference pattern formed by a thin film and derive the conditions for constructive and destructive interference.
+    31. Solve for the diffraction pattern produced by a circular aperture.
+    32. Calculate the phase shift introduced by a birefringent material and determine the resulting polarization state.
+    33. Analyze the diffraction pattern for a diffraction grating and compute the angles of diffraction for different orders.
+    34. Solve for the transmission and reflection of polarized light through a series of polarizers at various angles.
+    """)
+
+# Week 7-8: Electromagnetic Radiation
+with st.expander("**Week 7-8: Electromagnetic Radiation: Retarded Potentials, Lienard-Wiechert Potentials**"):
+    st.markdown("""
+    ### Topics Covered
+    - Retarded Potentials: Deriving and understanding scalar and vector potentials in time-dependent situations.
+    - Lienard-Wiechert Potentials: Potentials and fields from moving charges, including radiation.
+    - Radiation from Accelerating Charges: Dipole radiation, quadrupole radiation, and radiation patterns.
+
+    ### Problems
+    35. Derive the retarded scalar and vector potentials for a moving point charge.
+    36. Compute the Lienard-Wiechert potentials for a uniformly moving charge and derive the corresponding electric and magnetic fields.
+    37. Solve for the radiation field produced by a harmonically oscillating dipole.
+    38. Calculate the total power radiated by a point charge undergoing uniform acceleration.
+    39. Derive the angular distribution of the radiation emitted by a dipole antenna.
+    40. Compute the radiation intensity of a dipole antenna as a function of distance and angle.
+    41. Derive the electric and magnetic fields of a moving point charge using the Lienard-Wiechert potentials.
+    42. Analyze the radiation emitted by a charge moving in a circular orbit and derive the synchrotron radiation.
+    43. Calculate the electric field of a moving dipole at a point far from the source.
+    44. Derive the fields of a charge moving with uniform velocity in the near and far zones.
+    """)
+
+# Week 9: Radiation from Moving Charges
+with st.expander("**Week 9: Radiation from Moving Charges**"):
+    st.markdown("""
+    ### Topics Covered
+    - Power radiated by accelerating charges: Larmor’s formula.
+    - Angular distribution of radiation.
+    - Synchrotron radiation and bremsstrahlung.
+
+    ### Problems
+    45. Derive Larmor’s formula for the total power radiated by a non-relativistic accelerating charge.
+    46. Calculate the angular distribution of radiation from an accelerating charge and compare it to the dipole radiation pattern.
+    47. Compute the radiation emitted by a charged particle undergoing circular motion (synchrotron radiation).
+    48. Analyze bremsstrahlung radiation emitted when a high-energy electron is decelerated by a nucleus.
+    49. Solve for the energy spectrum of synchrotron radiation from relativistic particles in a magnetic field.
+    50. Derive the expression for the radiation reaction force experienced by an accelerating charge.
+    51. Calculate the radiation emitted by a relativistic electron spiraling in a magnetic field.
+    52. Analyze the radiation fields produced by a charge oscillating in a harmonic potential.
+
+    ### Topics Covered
+    - Lorentz Transformations: Understanding four-vectors and Lorentz transformations in special relativity.
+    - Electromagnetic Field Tensor: Covariant formulation of Maxwell’s equations using the field tensor.
+    - Relativistic Electromagnetic Fields: Transformations of electric and magnetic fields under Lorentz transformations.
+
+    ### Problems
+    53. Derive the Lorentz transformations for the electric and magnetic fields between two inertial frames.
+    54. Solve for the electromagnetic field tensor and show how Maxwell’s equations are expressed in covariant form.
+    55. Calculate the electric and magnetic fields of a moving charge using the relativistic Lienard-Wiechert potentials.
+    56. Derive the four-potential for a moving point charge and show how it transforms under Lorentz transformations.
+    57. Solve for the transformation of the electromagnetic wave equation under Lorentz boosts.
+    58. Derive the energy-momentum tensor for the electromagnetic field and show how it leads to conservation laws.
+    59. Analyze the relativistic Doppler effect for an electromagnetic wave moving towards and away from a source.
+    60. Calculate the relativistic field transformation for a charged particle moving at near-light speed.
+    """)
+
+# Week 12-13: Applications of Electromagnetic Theory to Modern Physics
+with st.expander("**Week 12-13: Applications of Electromagnetic Theory to Modern Physics**"):
+    st.markdown("""
+    ### Topics Covered
+    - Electromagnetic Fields in Astrophysics: Applications to star formation, pulsars, and black holes.
+    - Quantum Electrodynamics (QED): Basic principles and interaction of photons and electrons.
+    - Electromagnetic Theory in Plasma Physics: Behavior of charged particles in a plasma; Debye shielding and plasma oscillations.
+
+    ### Problems
+    61. Solve for the electromagnetic field around a neutron star using Maxwell’s equations and relativistic corrections.
+    62. Analyze the interaction between a photon and an electron in a basic quantum electrodynamics (QED) process, such as Compton scattering.
+    63. Calculate the behavior of electromagnetic waves in a plasma and derive the dispersion relation.
+    64. Solve for the radiation emitted by a rapidly spinning pulsar using relativistic electromagnetic theory.
+    65. Analyze the interaction between the cosmic microwave background radiation and charged particles in space.
+    66. Derive the electromagnetic field generated by a rotating black hole using the Kerr metric.
+    67. Solve for the energy lost to radiation in the early universe and its effects on the cosmic expansion.
+    68. Compute the fields produced by a magnetar and analyze the effects of extreme magnetic fields on the surrounding plasma.
+    69. Analyze the behavior of electromagnetic fields in a high-energy astrophysical plasma.
+    70. Solve for the electromagnetic fields of a charged particle moving in the strong gravitational field of a black hole.
+    """)
+
+# Week 14: Advanced Topics in Plasma Physics and Magnetohydrodynamics
+with st.expander("**Week 14: Advanced Topics: Plasma Physics and Magnetohydrodynamics (MHD)**"):
+    st.markdown("""
+    ### Topics Covered
+    - Plasma Physics: Understanding Debye shielding, plasma oscillations, and wave propagation in plasmas.
+    - Magnetohydrodynamics (MHD): Application of MHD equations to plasma flows and astrophysical systems.
+    - Alfven Waves: Study of MHD waves and their role in plasma dynamics.
+
+    ### Problems
+    71. Derive the dispersion relation for plasma oscillations in a cold plasma and interpret its physical significance.
+    72. Solve for the Debye length in a plasma and analyze its implications for electrostatic shielding.
+    73. Compute the Alfven wave velocity in a magnetized plasma and analyze its behavior in an MHD system.
+    74. Derive the MHD equations for a plasma and solve for the magnetic pressure and tension forces.
+    75. Analyze the stability of an MHD pinch and solve for the conditions for stability.
+    76. Solve for the energy density and flux of Alfven waves in a conducting plasma.
+    77. Derive the equations governing the propagation of electromagnetic waves in a hot plasma.
+    78. Solve for the effects of magnetic reconnection on the stability of an astrophysical plasma.
+    """)
+
+# Week 15: Review and Final Exam Preparation
+with st.expander("**Week 15: Review and Final Exam Preparation**"):
+    st.markdown("""
+    ### Topics Covered
+    - Comprehensive Review: Review of electromagnetic wave theory, radiation, and covariant formulation of Maxwell’s equations.
+    - Problem-Solving Sessions: Focus on solving complex problems that integrate multiple course concepts.
+    - Final Exam Preparation: Students will receive guidance on tackling exam problems, with a focus on key concepts and application-based questions.
+
+    ### Problems
+    79. Solve for the propagation of an electromagnetic wave in a dispersive medium and compare phase and group velocities.
+    80. Analyze the radiation pattern and power emitted by a relativistic electron spiraling in a magnetic field.
+    """)
+
+# Textbooks Section
+st.markdown("""
+## Textbooks
+- **Classical Electrodynamics** by John David Jackson  
+- **Introduction to Electrodynamics** by David J. Griffiths
+""")