In a vacuum electromagnetic wave, what is the relation between the magnetic field amplitude B and the electric field amplitude E?

In a vacuum electromagnetic wave, what is the relation between the magnetic field amplitude B and the electric field amplitude E?

• A. B = E c
• B. B = E / c^2
• C. B = E / c
• D. B = μ0 E

Answer: (C)

In a vacuum EM wave, the electric and magnetic fields propagate together and are perpendicular to each other and to the direction of travel. The wave speed is c, and Maxwell’s equations for a plane wave lead to a relationship between the fields where the magnitude of the electric field is c times the magnitude of the magnetic field. Put differently, |E| = c|B|, so the magnetic-field amplitude is the electric-field amplitude divided by c. This also aligns with energy considerations: the energy density stored in the electric field equals that in the magnetic field, since ε0E^2/2 = B^2/(2μ0) and c^2 = 1/(μ0ε0), giving E = cB or B = E/c.

In a vacuum EM wave, the electric and magnetic fields propagate together and are perpendicular to each other and to the direction of travel. The wave speed is c, and Maxwell’s equations for a plane wave lead to a relationship between the fields where the magnitude of the electric field is c times the magnitude of the magnetic field. Put differently, |E| = c|B|, so the magnetic-field amplitude is the electric-field amplitude divided by c. This also aligns with energy considerations: the energy density stored in the electric field equals that in the magnetic field, since ε0E^2/2 = B^2/(2μ0) and c^2 = 1/(μ0ε0), giving E = cB or B = E/c.