Question

The magnetic field in a plane monochromatic electromagnetic wave with wavelength λ = 684 nm, propagating in a vacuum in the z-direction is described by

B⃗ =(B1sin(kz−ωt))(i^+j^)B→=(B1sin⁡(kz−ωt))(i^+j^)

where B₁ = 5.3 X 10^-6 T, and i-hat and j-hat are the unit vectors in the +x and +y directions, respectively.

1)

What is k, the wavenumber of this wave?

m^-1

2)

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?

nm

3)

What is E_max, the amplitude of the electric field oscillations?

V/m

4)

What is E_y, the y-component of the electric field at (x = 0, y-0, z = z_max) at t = 0?

V/m

Answer 1

Given wavelength = 684nm

B =

where = where are the unit vectors in the +x and +y directions respectively.

1.

The wavenumber of this wave k

2.

The distance along the positive z-axis to the position where the magnitude of the magnetic field is a maximum at t = 0 i.e

When ,

from 1

on substitution of values

Z= 171nm

3.

The amplitude of the electric field oscillations ​​​​​​

Where c is the speed of light

= √2 *

4.

The y-component of the electric field at (x = 0, y=0, z = ) at t = 0

The projection on y ,it will form a triangle at one of the angle is 45°

So

from 3

on substitution of values

in -ve direction.