91Ó°ÊÓ

The electric field component $E_z=\left(2.0\text{V/m}\right)\cos \left[\left(\mathrm{π}×{10}^{15}{\text{s}}^{-1}\right)\left(t-x/c\right)\right]$.

The electric and magnetic fieldsandare always perpendicular to the direction in which the wave is traveling.

The electric and magnetic fields are related as, $c=\frac{E_z}{B_y}$

The electric and magnetic fields E and B are always perpendicular to the direction in which the wave travels.

The plane electromagnetic wave is traveling in x direction hence $E_x$and $E_y$are zero.

From the given, the electric field is in the z direction; hence the magnetic field is in the y direction.

The electric and magnetic fields are related as,

$c=\frac{E_z}{B_y}$

Hence, the amplitude of the magnetic field will be,

$B_y=\frac{E_z}{c}$

Where the speed of the light is, $c=3×{10}^8\text{m/s}$.

Substitute the values in the above expression, and we get,

role="math" localid="1662971654502" $\begin{array}{rcl}{B}_y& =& \frac{2.0\text{V/m}}{3×{10}^8\text{m/s}}\\ B_y& =& 6.67×{10}^{-9}\mathrm{T}\\ & =& 6.7\mathrm{nT}\end{array}$

Thus, theamplitude of the magnetic field component is $6.7\mathrm{nT}$.

The EM wave is traveling in the x direction. The electric field component is in the z-direction.

Hence, the magnetic field component will oscillate in the y direction.

From Faraday’s law of induction, the direction of the magnetic field is –y when the electric field is in the +z direction.

Thus, the direction of the magnetic field is –y.