Magnetism & induction

The big picture

A magnetic force can curve the path of a charge without changing its speed. Induction introduces a different mechanism: a changing flux or moving conductor can produce an emf. Keep the force question and the energy-transfer question distinct.

Choose directions before calculating magnitudes. Mark the loop normal, the positive circulation and the field direction, then let the signs carry the argument. Alternating circuits extend that bookkeeping to phase rather than only plus and minus.

What to read, and why

Start at the first stage if the subject is new. Otherwise, use the descriptions to find the missing step in your understanding. All chapter explanations are open; the labels identify chapters whose solutions and answer checks are also free.

1. STAGE 1

   From force to changing flux

   Separate the force on a moving charge from an induced emf, with explicit directions and an energy account.

   Magnetic forces, selected velocities and current-produced fields →Use cross products for direction, circular dynamics for motion and Biot–Savart geometry for field sources.13 worked examples · 11 checks · Complete free chapterInduction, moving conductors and magnetic energy →Follow the changing flux, establish the sign, and close the energy account.16 worked examples · 12 checks · Open explanation · member practice

2. STAGE 2

   Connect induction and phase

   Understand AC reactance before transformers, then connect inductive and capacitive energy in oscillating circuits.

   Alternating circuits: phase, RMS and real power →Build the circuit response from derivatives, then use phasors and energy to check it.9 worked examples · 8 checks · Open explanation · member practiceCoupled coils and transformer reasoning →Track shared flux, winding polarity, stored energy and the load seen by the source.7 worked examples · 6 checks · Open explanation · member practiceFrom LC energy exchange to RLC resonance →Connect charge, current, phase and loss without confusing three different frequencies.7 worked examples · 5 checks · Open explanation · member practice

3. STAGE 3

   Connect fields and matter

   Extend the field picture to material response and displacement current.

   Magnetic moments, materials and hysteresis →Connect microscopic alignment to measurable fields, sample geometry and energy loss.7 worked examples · 5 checks · Open explanation · member practiceFrom changing electric fields to electromagnetic waves →Resolve the capacitor-gap puzzle, derive the wave speed and follow energy through the fields.7 worked examples · 8 checks · Open explanation · member practice

Choose a method before an equation

Use the physical conditions to narrow the choices. A formula becomes useful after you know why its model applies.

Try a complete free problem

These problems include the hints, worked reasoning and answer feedback. Attempt one before opening the solution.