Physics
Electromagnetic Induction
A changing magnetic flux through a loop induces an EMF (voltage). Faraday's law: EMF = -dΦ/dt, where Φ = B·A·cos(θ). Lenz's law says the induced current flows in whichever direction opposes the change. Together they explain generators, transformers, and induction cooktops.
How to Approach Electromagnetic Induction
Compute the flux Φ
Φ = B·A·cos(θ), where B is the magnetic field, A is the area of the loop, and θ is the angle between B and the loop's normal. Watch units — Φ is in webers (Wb = T·m²).
Take the time derivative
EMF = -dΦ/dt. The flux can change because B changes, A changes (loop expands/contracts), or θ changes (loop rotates — this is how generators work).
Apply Lenz's law for direction
The induced current flows in whatever direction creates a magnetic field opposing the change in flux. If flux is increasing upward, induced current creates a downward field.
Frequently Asked Questions
Why is there a minus sign?+
Lenz's law — encoded as the negative sign — says induced currents oppose the change in flux. It's a consequence of energy conservation; without it, you could build a perpetual motion machine.
What's motional EMF?+
When a conductor moves through a magnetic field, charges in it experience a magnetic force. For a rod of length L moving at v through field B: EMF = B·L·v. It's a special case of Faraday's law.
How does a transformer work?+
AC current in the primary coil creates a time-varying flux. That flux induces an EMF in the secondary coil, scaled by the ratio of turns: V_secondary/V_primary = N_secondary/N_primary.
Related Topics
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