Answer:
[tex]-5.78414\times 10^{-6}\ T[/tex]
Explanation:
[tex]\epsilon_0[/tex] = Permittivity of free space = [tex]8.85\times 10^{-12}\ F/m[/tex]
c = Speed of light = [tex]3\times 10^8\ m/s[/tex]
[tex]\lambda[/tex] = Wavelength = 0.3 m
T = Time period
f = Frequency
[tex]E_0[/tex] = Electric field
Intensity of electric field is given by
[tex]I=\dfrac{1}{2}c\epsilon_0E_0^2\\\Rightarrow E_0=\sqrt{\dfrac{2I}{c\epsilon_0}}\\\Rightarrow E_0=\sqrt{\dfrac{2\times 45}{3\times 10^{8}\times 8.85\times 10^{-12}}}\\\Rightarrow E_0=184.11492\ N/C[/tex]
Magnetic field is given by
[tex]B_0=\dfrac{E_0}{c}\\\Rightarrow B_0=\dfrac{184.11492}{3\times 10^8}\\\Rightarrow B_0=6.13716\times 10^{-7}\ T[/tex]
[tex]k=\dfrac{2\pi}{\lambda}\\\Rightarrow k=\dfrac{2\pi}{0.3}\\\Rightarrow k=20.94\ /m[/tex]
[tex]f=\dfrac{c}{\lambda}\\\Rightarrow f=\dfrac{3\times 10^{8}}{0.3}\\\Rightarrow f=1\times 10^{9}\ Hz[/tex]
[tex]T=\dfrac{1}{f}\\\Rightarrow T=10^{-9}[/tex]
[tex]\omega=\dfrac{2\pi}{T}\\\Rightarrow \omega=\dfrac{2\pi}{10^{-9}}\\\Rightarrow \omega=6283185307.17958\ rad/s[/tex]
Magnetic field in the z direction is given by (x=0)
[tex]B_z=B_0(kx-\omega t)\\\Rightarrow B_z=6.13716\times 10^{-7}\times (0-6283185307.17958\times 1.5\times 10^{-9})\\\Rightarrow B_z=-5.78414\times 10^{-6}\ T[/tex]
The magnetic field at the origin is [tex]-5.78414\times 10^{-6}\ T[/tex]
