A plane EM wave is propagating along x direction. It has a wavelength of 4 mm. If electric field is in y direction with the maximum magnitude of 60 V m⁻¹, the equation for magnetic field is:
Options

Question

A plane EM wave is propagating along x direction. It has a wavelength of 4 mm. If electric field is in y direction with the maximum magnitude of 60 V m⁻¹, the equation for magnetic field is:

G1 Physics · Accepted Answer

For an electromagnetic wave: E₀ = cB₀ Therefore: B₀ = E₀/c = 60/(3 × 10⁸) = 2 × 10⁻⁷ T Wavelength: λ = 4 mm = 4 × 10⁻³ m Wave number: k = 2π/λ = 2π/(4 × 10⁻³) = (π/2) × 10³ rad/m The wave travels along +x and the electric field is along +y. For propagation direction: E × B = +x Therefore magnetic field is along +z. Hence: B(z) = 2 × 10⁻⁷ sin[(π/2) × 10³(x - 3 × 10⁸t)] k̂ T