If B and K represent the magnetic field and propagation vectors of an electromagnetic wave in vacuum, which of the following gives the correct expression for the electric field vector E ? (Here is the angular frequency and k is the magnitude of the propagation vector)

Step-by-step solution

The relationship between the magnetic field, electric field, and propagation vector is given by: B = 1 ( K E ) Taking the cross product of K with both sides: K B = 1 [ K ( K E )] Using the vector triple product expansion A ( B C ) = ( A C ) B - ( A B ) C : K B = 1 [( K E ) K - ( K K ) E ] For an electromagnetic wave, the electric field is perpendicular to the propagation vector, so K E = 0 . Also, the magnitude squared of the propagation vector is K K = k^2 . K B = 1 [0 - k^2 E ] = - k^2 E Rearranging for E : E = -