Chapter 17: The Laws of Induction & Electromagnetic Force

The Laws of Induction & Electromagnetic Force physics chapter provides a deep examination of electromagnetic induction, clarifying how Faraday's law represents two distinct physical mechanisms often grouped under the general "flux rule". The text distinguishes the electromotive force (emf) produced by charges moving within a static magnetic field (the velocity cross B force) from the emf generated by a time-varying magnetic field, which creates an induced electric field (where the curl of E equals the negative partial derivative of B with respect to time). Several key examples illustrate situations where the simple flux rule is insufficient, such as the behavior of rotating copper discs. A significant application of the induced electric field mechanism is detailed through the operation of the betatron, a particle accelerator that maintains a stable circular orbit while accelerating electrons. The unique condition for betatron function is derived, showing that the average magnetic field inside the electron's orbit must be precisely twice the magnetic field magnitude at the radius of the orbit. The chapter also discusses an intriguing paradox involving a solenoid and a disc, resolving it through the careful application of the fundamental laws of physics, including the conservation of angular momentum. Practical applications are explored, specifically the function of the alternating-current (AC) generator, where the rotation of a coil in a uniform magnetic field produces a sinusoidally time-varying emf. Finally, the discussion moves to circuit elements, defining mutual inductance (M) between two coils and self-inductance (L) within a single circuit. Analogies are drawn comparing self-inductance to mass (inertia) in mechanics and current to velocity. This framework leads to the quantification of the magnetic energy stored in an inductor, U equals one-half times L times I squared, and concludes with the generalization of magnetic energy stored in a volume of space, proportional to the integral of the magnetic field squared.