Question

The magnetic field in a plane monochromatic electromagnetic wave with wavelength vacuum in the z-direction is described by - 561 nm, propagating in a B = (B1 sin(kz - @))i + where B1 - 6.8 x 10-6 T, and i-hat and j-hat are the unit vectors in the +x and y directions, respectively.

Answer 1

At x=y=z=0,

$\vec{B}=B_{1}sin(-\omega t)(\hat{i}+\hat{j})$

For B to be maximum,

$\omega t_{max}=\frac{\pi }{2}$

$t_{max}=\frac{\pi }{2*\omega }=\frac{\pi }{2*2*\pi*frequency }=\frac{1}{4*frequency }$

$frequency=\frac{c}{\lambda }=\frac{3*10^{8}}{561*10^{-9}}=5.35*10^{14}\ Hz$

$t_{max}=\frac{1}{4*5.35*10^{14}}=4.67*10^{-16}\ seconds$