Physics Education & Conceptual Laboratory
Curated notes, mathematical derivations, and physical intuition by Asit Purohit.
1. Classical Mechanics: The Work-Energy Theorem
The foundation of physical mechanics relies on energy conservation derived directly from Newton's second law.
Definition of Mechanical Work:
W = \int_{A}^{B} \vec{F} \cdot d\vec{r}
Work-Energy Relation:
W_{\text{net}} = \Delta K = \frac{1}{2}m v_f^2 - \frac{1}{2}m v_i^2
2. Electromagnetism: Maxwell's Equations in Integral Form
Electric and magnetic fields form a unified gauge-invariant tensor in spacetime:
Gauss's Law\oint \vec{E} \cdot d\vec{A} = \frac{Q_{\text{encl}}}{\varepsilon_0}
Gauss's Law for Magnetism\oint \vec{B} \cdot d\vec{A} = 0
Faraday's Law\oint \vec{E} \cdot d\vec{s} = -\frac{d\Phi_B}{dt}
Ampère-Maxwell Law\oint \vec{B} \cdot d\vec{s} = \mu_0 I + \mu_0\varepsilon_0 \frac{d\Phi_E}{dt}
Interactive Simulations on MetaMotion
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