An electromagnetic wave has an electric field given by the expression (in Cartesian co-ordinates) : E → ( x , t ) = 6.0 cos ⁡ ( 1.4 × 10 7 x − 3.43 × 10 15 t ) z ^ . What is the direction of the magnetic field at time t = 0 and position x = 0 ? A. -x B. +x C. -y D. +y

Question

An electromagnetic wave has an electric field given by the expression (in Cartesian co-ordinates) :             E      →        (  x  ,  t  )  =  6.0  cos  ⁡  (  1.4  ×      10    7    x  −  3.43  ×      10          15        t  )            z      ^      . What is the direction of the magnetic field at time t = 0 and position x = 0 ? A. -x B. +x C. -y D. +y

Collin Johns · Accepted Answer

∵            E      →        ×            B      →            |        |              V      →        where             V      →       is a representation of the direction of propagation. Given that wave is propagating along + x-axis and             E      →       along z-axis. Therefore             E      →        ×            B      →        =  +            i      ^        ⇒            k      ^        ×            B      →        =  +            i      ^        ⇒            B      →      is along  −            j      ^