If E⃗  and K⃗  represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by:(ω− angular frequency)

The magnetic field vector B⃗ in an electromagnetic wave is given by the cross product of the propagation vector (K⃗) and the electric field vector (E⃗). This can be mathematically represented as:

B⃗ = K⃗ x E⃗ / ω

Where:

• B⃗ is the magnetic field vector
• K⃗ is the propagation vector
• E⃗ is the electric field vector
• ω is the angular frequency

This equation is derived from Maxwell's equations and the wave equation for electromagnetic waves. It shows that the magnetic field vector is perpendicular to both the direction of propagation and the electric field vector.