An electromagnetic wave is traveling through vacuum in the positive x direction. Its electric field vector is given by E⃗ =E0sin(kx−ωt)j^,where j^ is the unit vector in the y direction. What is the Poynting vector S⃗ (x, t), that is, the power per unit area associated with the electromagnetic wave described in the problem introduction?

Given that,

The electric field is given by,

Suppose, B is the amplitude of magnetic field vector.

We need to find the complete expression for the magnetic field vector of the wave

Using formula of magnetic field

Direction of vector is the direction of propagation of the wave .

Direction of magnetic field =

We need to calculate the poynting vector

Using formula of poynting

Put the value into the formula

Hence, The poynting vector is