Faraday's law of electromagnetic inductionlaw
Michael Faraday in 1831 long sought a connection between magnetism and electricity. His ingenious experiment with two windings on one iron ring showed: when current was switched on in the first coil, a momentary surge appeared in the second. He described it as 'converting magnetism into electricity.' Later, James Clerk Maxwell put the law into rigorous mathematical form. The essence: any change in a magnetic field over time generates a vortex electric field, even in a vacuum.
How it works
A bicycle dynamo: a magnet spins near a coil, the magnetic flux constantly changes, and the light bulb glows. In a wall outlet, alternating current comes through a transformer, where one coil changes the field and induces current in another, stepping down or up the voltage.
💡 If you drop a strong magnet into a copper pipe, it falls surprisingly slowly — induced currents (eddy currents) according to Lenz's law slow it down, as if an invisible hand is holding it.
\mathcal{E} = -\frac{d\Phi_B}{dt}
ℰ — electromotive force (EMF) of induction (V), Φ_B — magnetic flux (Wb), equal to ∫_S B·dA, B — magnetic induction (T), A — surface area (m²), t — time (s); the minus sign indicates direction according to Lenz's rule
\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}
∇ × E — curl of the electric field (V/m²), ∂B/∂t — partial derivative of magnetic induction with respect to time (T/s)