Question

A slab (pulse) of electromagnetic radiation that is 15cm thick is propagating downward (in the direction) toward a short horizontal copper wire located at the origin and oriented parallel to the z axis, as shown in Figure 23.123. (a) The direction of the electric field inside the slab is out of the page (in the$\mathbf{+}\mathbf{}\mathit{z}$ direction). On a diagram, show and describe clearly the direction of the magnetic field inside the slab.

(b) You stand on the x axis at location$<12,0,0>\mathbf{}\mathit{m}$, at right angles to the direction of propagation of the pulse. Your friend stands on the z axis at location$<0,0,12>\mathbf{}\mathit{m}$. The pulse passes the copper wire at time ${\mathit{t}}_{\mathbf{1}}\mathbf{=}\mathbf{0}$, and at a later time ${\mathit{t}}_{\mathbf{2}}$ you observe new nonzero electric and magnetic fields at your location, but your friend does not. Explain. What is ${\mathit{t}}_{\mathbf{2}}$? (Give a numerical answer.) How long a time do these new fields last for you? (c) On a diagram, show and describe clearly the directions of these new nonzero fields ($\overrightarrow{\mathbf{E}}$ and $\overrightarrow{\mathbf{B}}$) at your location. Explain briefly but carefully.

Short answer

The direction of the magnetic field inside the slab is in the negative x axis.

Step-by-step solution

Write the given data from the question.

Thickness of the slab(pulse),$L=15\text{cm}$

Pulse is propagated is$-y$ direction.

The direction of the electric field inside the slab is out of the page.

Determine the formulas to show the direction of the magnetic field inside the slab.

The expression to determine the direction of the propagated wave is given as follows.

$\mathit{k}\mathbf{=}\overrightarrow{\mathbf{E}}\mathbf{\times }\overrightarrow{\mathbf{B}}$ …… (i)

Here,$\overrightarrow{\mathbf{E}}$ is the electric field and$\overrightarrow{\mathbf{B}}$ is the magnetic field.

Show the direction of the magnetic field inside the slab.

The direction of the electric field inside the slab is out of the page or$+z$ direction and wave is propagated in the negative y direction.

The direction of the propagated wave is calculated by the cross product of the vector electric field and vector magnetic field. Therefore, the direction of the magnetic field inside the slab must be in the negative axis.

The below figure shows the direction of the magnetic field.

Hence the direction of the magnetic field inside the slab is in the negative x-axis.