Electromagnetic Induction – Naming the law The statement “A time-varying magnetic field produces an electric field” refers to which fundamental law of electromagnetism?

Introduction / Context:
Remote sensing instruments, antennas, and scanning electronics all rely on Maxwell’s equations. Recognizing which law links changing magnetic fields to induced electric fields is foundational for understanding wave generation and transformer/coil behaviour.

Given Data / Assumptions:

• Time-varying magnetic field B(t).
• Induced electric field E in space (non-electrostatic).

Concept / Approach:
Faraday’s law of induction states that a changing magnetic flux induces an electromotive force and a corresponding electric field, quantitatively expressed in integral or differential form (curl E is proportional to the negative time derivative of B).

Step-by-Step Solution:
Identify cause: dB/dt ≠ 0.Result: rotational electric field E appears (induction).Associate with formal name: Faraday’s law.

Verification / Alternative check:
Complementary law: Ampère–Maxwell relates changing electric field to magnetic field (displacement current), not vice versa, confirming the specific attribution to Faraday for E from dB/dt.

Why Other Options Are Wrong:

• Newton/Kirchhoff/Coulomb: mechanics/circuit/statics laws not describing induction.
• Ampère–Maxwell law addresses B from changing E or current density.

Common Pitfalls:
Swapping Faraday’s and Ampère–Maxwell’s roles when recalling the curl equations.

Final Answer:
Faraday's law