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#field symmetry

2 public questions tagged with this topic.

In electromagnetic wave theory, what ensures the symmetry between electric and magnetic fields in wave propagation?

**EM wave in vacuum** transverse, E and B perpendicular to propagation and to each other, E×B along propagation, in phase, E/B = c =3×10⁸ m/s, c =1/√(μ₀ ε₀), μ₀=4π×10⁻⁷ H/m, ε₀=8.85×10⁻¹² F/m. For E₀=45 V/m, B₀=E₀/c=45/3×10⁸=1.5×10⁻⁷ T=150 nT, illustrating B much smaller than E. Faraday’s law and the Ampere-Maxwell law together ensure symmetry, as a changing electric field induces a magnetic field and vice versa, sustaining wave propagation. Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum classification λ = c/f, evaluation yields Faraday’s and Ampere-Maxwell laws, illustrating EM wave

Ref: NCERT > Physics Book > Electromagnetic Waves > EM Wave Characteristics - Transverse Nature and E/B Ratio

What insight does the Ampere-Maxwell law provide about the symmetry of electromagnetic fields?

**Displacement current** I_d = ε₀ dΦ_E/dt, Φ_E = ∫ E·dA electric flux (V·m), ε₀=8.85×10⁻¹² F/m, ensures continuity of current in charging capacitor where conduction current stops between plates, I_d equals conduction current in wires, 3 A conduction ⇒ 3 A displacement, maintaining Ampere's law ∮ B·dl = μ₀(I_c+I_d). The Ampere-Maxwell law shows that just as a changing magnetic field induces an electric field (Faraday’s law), a changing electric field induces a magnetic field, highlighting the symmetry in electromagnetic interactions. Using c = fλ, E₀/B₀ = c, I_d = ε₀ dΦ_E/dt, and spectrum class

Ref: NCERT > Physics Book > Electromagnetic Waves > Displacement Current and Ampere-Maxwell Law