Electromagnetics – Name the law: time-varying E-field generates B-field A time-varying electric field produces a magnetic field. What is this phenomenon called in electromagnetic field theory?

Introduction / Context:
Maxwell unified electricity and magnetism by adding the displacement current term to Ampere’s circuital law. This addition states that a changing electric field acts like a current and produces a magnetic field, enabling electromagnetic wave propagation even in free space.

Given Data / Assumptions:

• Classical electromagnetic theory in macroscopic form.
• Time-varying fields; no need for material currents for the effect to exist.
• Free space or linear media.

Concept / Approach:

The Ampere–Maxwell law augments Ampere’s law by adding the displacement current density term epsilon * dE/dt. Thus, even where conduction current is absent, a changing electric field produces magnetic field circulation. By symmetry, Faraday’s law states the dual effect: a changing magnetic field induces an electric field.

Step-by-Step Solution:

Verification / Alternative check:

Wave equation derivation uses both laws; the displacement current term is essential for continuity of current in capacitors and for wave propagation.

Why Other Options Are Wrong:

Faraday’s law is the magnetic-to-electric counterpart; Hertz verified waves experimentally but did not provide the governing law; Kirchhoff and Coulomb address other regimes.

Common Pitfalls:

Swapping Faraday’s and Ampere–Maxwell roles; assuming a conduction current is required to generate magnetic fields in time-varying regimes.

Final Answer:

Ampere–Maxwell law