ISEGORIA / MATH ENCYCLOPEDIA
Electromagnetism: fields and induction
Electric fields, magnetic forces, and changing flux.
Before you begin: Vectors and calculus
Predict, manipulate, then check your reasoning against the example and question. Graphs illustrate the mathematics; they do not replace a proof.
1. Electric field lines
Move two charges and inspect the vector field and equipotential contours.
Worked example. Field lines leave positive charges and enter negative charges.
Watch out. The point-charge field diverges at the charge location.
How is direction encoded?
By arrows aligned with the local electric field vector.
2. Lorentz force
Change velocity and magnetic field to see circular or helical motion.
Worked example. A velocity perpendicular to B bends continuously; parallel velocity is unchanged.
Watch out. The nonrelativistic model assumes speeds well below c.
Which component does magnetic force not change?
The component of velocity parallel to the magnetic field.
3. Faraday induction
Sweep a magnet through a loop and track flux, induced emf, and current direction.
Worked example. Faster flux change produces larger induced emf.
Watch out. The loop is idealized with constant resistance and no self-inductance.
Why is there a minus sign?
Lenz’s law: the induced effect opposes the flux change.