Apply Ampère's law $\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{enc}$ to calculate magnetic fields in symmetric configurations. Visualize magnetic field patterns inside solenoids, toroids, and around current-carrying wires using closed loop integration.
Calculate electric potential $V = \frac{kQ}{r}$ and potential energy $U = qV$ for point charges and charge distributions. Visualize equipotential surfaces, explore the relationship $\vec{E} = -\nabla V$, and analyze how charges move from high to low potential.
Explore the four Maxwell's equations that unify electricity and magnetism: Gauss's law, Gauss's law for magnetism, Faraday's law, and Ampère-Maxwell law. Visualize how these equations predict electromagnetic wave propagation and the interconnection between electric and magnetic fields.
Explore capacitance $C = \frac{Q}{V}$ and how dielectric materials increase capacitance by reducing the electric field. Visualize energy storage $U = \frac{1}{2}CV^2$ in parallel-plate capacitors and analyze the effects of dielectric constant on charge distribution.
Visualize the differential oscillation of energy between an inductor's magnetic field and a capacitor's electric field. Live graphs of charge and current.