Electromagnetic radiation — identify the incorrect statement Which one of the following statements about the origin and coupling of electromagnetic (EM) fields is incorrect?

Introduction / Context:Electromagnetic radiation emerges from time-varying electric charges and currents. Maxwell’s equations link electric and magnetic fields so that changes in one generate the other, enabling wave propagation through space (and many media) without a material carrier.

Given Data / Assumptions:

• Classical EM theory in free space or simple media.
• Non-relativistic descriptions are adequate for these qualitative statements.
• We are testing conceptual correctness, not numerical computation.

Concept / Approach:

Accelerating charges and time-varying currents produce time-varying electric and magnetic fields. Faraday’s law links changing magnetic flux to induced electric fields; Maxwell-Ampère’s law links changing electric fields (displacement current) and currents to magnetic fields. Together these form coupled wave equations describing EM radiation. Hence statements (a)–(c) correctly summarize fundamental physics; there is no incorrect choice among them, so “None of these” is the correct selection for “which is incorrect?”.

Step-by-Step Solution:

Verification / Alternative check:

Deriving the wave equation from Maxwell’s equations yields ∇^2E − μϵ ∂^2E/∂t^2 = 0 and the analogous form for B, confirming mutual coupling and propagation. (Symbolic mention only; no detailed math required here.)

Why Other Options Are Wrong:

• Selecting any of (a)–(c) as incorrect would contradict Maxwellian electrodynamics.

Common Pitfalls:

• Assuming constant-velocity charges radiate; radiation requires acceleration.
• Imagining E or B can exist independently in a propagating wave; in free space they are coupled and transverse.

Final Answer:

None of these.