Analyze Magnetic Field

Solve problems involving changing magnetic flux using Faraday's law, Lenz's law, motional EMF, mutual and self-inductance, and RL circuit transients. Use when computing induced EMF from time-varying B-fields or moving conductors, determining current direction via Lenz's law, analyzing inductance and energy storage in magnetic fields, or solving RL circuit differential equations for switching transients.

Quantum physics simulation library for open quantum systems. Use when studying master equations, Lindblad dynamics, decoherence, quantum optics, or cavity QED. Best for physics research, open system dynamics, and educational simulations. NOT for circuit-based quantum computing—use qiskit, cirq, or pennylane for quantum algorithms and hardware execution.

Design practical electromagnetic devices including electromagnets, DC and brushless motors, generators, and transformers by bridging theory to application. Use when sizing a solenoid or toroidal electromagnet for a target field or force, selecting motor topology and computing torque and efficiency, designing a transformer for a given voltage ratio and power rating, or analyzing losses from copper resistance, core hysteresis, and eddy currents.

Work with the full set of Maxwell's equations in integral and differential form to analyze electromagnetic fields, waves, and energy transport. Use when applying Gauss's law, Faraday's law, or the Ampere-Maxwell law to boundary value problems, deriving the electromagnetic wave equation, computing Poynting vector and radiation pressure, solving for fields at material interfaces, or connecting electrostatics and magnetostatics to the unified electromagnetic framework.

Design and simulate a minimal CPU from scratch: define an instruction set architecture (ISA), build the datapath (ALU, register file, program counter, memory interface), design the control unit (hardwired or microprogrammed), implement the fetch-decode-execute cycle, and verify by tracing a small program clock cycle by clock cycle. The capstone "computer inside a computer" exercise that composes combinational and sequential building blocks into a complete processor.

Derive a theoretical result step-by-step from first principles or established theorems, with every step explicitly justified and special cases checked. Use when deriving a formula or theorem from first principles, proving a mathematical statement by logical deduction, re-deriving a textbook result for verification or adaptation, extending a known result to a more general setting, or producing a self-contained derivation for a paper or thesis.