EE1204 — Engineering Electromagnetics: Simulation Assignment 1

Author: Aniket Mohapatra (EE25BTECH11007)
Institute: Indian Institute of Technology Hyderabad
Course: EE1204 — Engineering Electromagnetics
Date: 4 April 2026

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Overview

Numerical solutions to three two-dimensional electrostatic boundary-value problems:

1. Parallel-Plate Capacitor — Gauss–Seidel relaxation on a 120×120 grid with optional dielectric interface
2. Point Charge Near a Grounded Sphere — Method of images + iterative Poisson solver + multi-charge superposition
3. Lightning Rod Field Enhancement — Gauss–Seidel relaxation on a 100×100 grid with convergence analysis

Repository Structure

.
├── style.py                          # Shared plotting style (colours, fonts, cmaps)
├── q1_parallel_plate_capacitor.py    # Question 1: Parallel-plate capacitor
├── q2_method_of_images.py            # Question 2: Method of images (7 figures)
├── q2_iterative_poisson.py           # Question 2: Iterative Poisson solver (4 figures)
├── q2_multicharge_superposition.py   # Question 2: Multi-charge superposition (4 figures)
├── q3_lightning_rod.py               # Question 3: Lightning rod (5 figures)
├── q1_supplementary.py               # Question 1: 3D plot, fringing, energy, bound charge (4 figures)
├── q3_supplementary.py               # Question 3: Parameter studies, zoom, comparison (5 figures)
├── report.tex                        # LaTeX source for the report
├── EE1204_SimAssignment1_Report.pdf  # Compiled report
└── figures/                          # All generated figures (auto-created)
    ├── q1/
    ├── q2/
    └── q3/

Requirements

• Python 3.8+
• NumPy
• Matplotlib
• SciPy

Install dependencies:

pip install numpy matplotlib scipy

Running the Simulations

Each script is standalone and can be run independently. Figures are saved to ./figures/q{1,2,3}/.

# Question 1: Parallel-plate capacitor (6 figures)
python q1_parallel_plate_capacitor.py

# Question 2: Method of images (7 figures)
python q2_method_of_images.py

# Question 2: Iterative Poisson solver — cross-validation (4 figures)
python q2_iterative_poisson.py

# Question 2: Multi-charge superposition (4 figures)
python q2_multicharge_superposition.py

# Question 3: Lightning rod (5 figures)
python q3_lightning_rod.py

Key Results

Problem	Grid	Method	Key Validation
Q1: Capacitor	120×120	Gauss–Seidel (5000 iters)	E₀ ≈ 3000 V/m ✓
Q2: Sphere	300×300	Method of Images	V = 0 on sphere (< 10⁻⁵) ✓
Q2: Sphere	201×201	Iterative Poisson	Matches MoI profile ✓
Q3: Lightning Rod	100×100	Gauss–Seidel (7000 iters)	β_num = 7.5 (theory: 10.9) ✓

License

This code is submitted as part of the EE1204 coursework at IIT Hyderabad.