An electromagnetic wave propagates in vacuum with a propagation vector K = c ( 3 2 i + 1 2 j ) and an electric field vector E = E₀ k . The corresponding magnetic field vector B is:

Step-by-step solution

The magnetic field vector is related to the electric field and propagation vectors by: B = 1 ( K E ) Substituting the given vectors into the expression: B = 1 [ c ( 3 2 i + 1 2 j ) E₀ k ] B = E₀ c [ 3 2 ( i k ) + 1 2 ( j k ) ] Using the standard cross product rules for unit vectors, i k = - j and j k = i : B = E₀ c ( - 3 2 j + 1 2 i ) B = E₀ c ( 1 2 i - 3 2 j ) Answer: E₀ c ( 1 2 i - 3 2 j )