The magnetic field in a plane monochromatic electromagnetic

The magnetic field in a plane monochromatic electromagnetic wave with wavelength lambda = 462 nm, propagating in a vacuum in the z-direction is described by B = (B_1 sin(kz - omega t))(I + j) where beta_1 = 9 5 times 10^-6 T and i-hat and j-hat are the unit vectors in the +x and +y directions, respectively What is k, the wavenumber of this wave? What is z_max, the distance along the positive z-axis to the position where the magnitude of the magnetic field is a maximum at t = 0? What is E_max the amplitude of the electric field oscillations? What is E_y, the y-component of the electric field at (x = 0, y = 0, z = z-max) at t = 0? Which of the following equations describes the spatial and time dependence of the electric field oscillations?

Solution

1. The value of wavenumber is k = 0.002164 nm^-1.

2. Value of Z_max = 0.182 nm

3. The value of amplitude of electric field oscillation is E_max  = 21 V/m

4. The y-component of electric field is equal to 1.8 V/m.