An electromagnetic wave is propagating along the positive z -axis. If the electric field vector is oscillating parallel to the vector ( i + j ) , which of the following represents a possible direction for the magnetic field vector?

Step-by-step solution

The direction of propagation of an electromagnetic wave is given by the direction of E B . Given that the wave propagates along the positive z -axis ( + k ) and the electric field E is parallel to ( i + j ) . Let us check the cross product for the given options: For option 1: ( i + j ) (- i + j ) = ( i - i ) + ( i j ) + ( j - i ) + ( j j ) = 0 + k - (- k ) + 0 = 2 k . This points in the +z direction, which matches the given propagation direction. For option 2: ( i + j ) ( i - j ) = - k - k = -2 k (points in -z dire