Apply Faraday's law $\mathcal{E} = -\frac{d\Phi_B}{dt}$ to calculate induced EMF from changing magnetic flux. Visualize how Lenz's law determines the direction of induced current to oppose flux changes, and explore applications in generators and transformers.
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.