In an air-filled rectangular waveguide with dimensions $a \times b$, the $\mathbf{TE}_{10}$ mode is transmitted. Given that the operating frequency is 5 GHz, $\lambda_{0} / \lambda_{c}=0.8$, and $b / a=0.5$, with an average transmitted power of 1 kW, what is the maximum value of each field component for this mode?

Options:
A. $$
\vert\ \dot{E}_{y} \vert_{\mathrm{m a x}}=\eta_{0} \Big( \frac{2 b} {\lambda_{0}} \Big) H_{\mathrm{o}}=\frac{b \mu_{0} b} {\pi} H_{\mathrm{o}}=5. 9 8 \times10^{4} \mathrm{~ V / m}
$$
$$
\left. \mid\dot{H}_{x} \mid_{\mathrm{m a x}}=\frac{\beta b H_{0}} {\pi} \mathrm{s i n} \left( \frac{\pi x} {b} \right) \right|_{z=b / 2}=\frac{2 b} {\lambda_{1}} H_{0}=9 5. 1 5 \quad\mathrm{A / m}
$$
$$
| \ \dot{H}_{z} \ |_{\mathrm{m a x}}=\left| H_{\circ} \mathrm{c o s} \Big( \frac{\pi x} {b} \Big) \right| |_{x=0, \, \pi}=H_{0}=1 2 6. \, 8 7 \quad\mathrm{A / m}
$$
B. $$
\vert\ \dot{E}_{y} \vert_{\mathrm{m a x}}=\eta_{0} \Big( \frac{3 b} {\lambda_{0}} \Big) H_{\mathrm{o}}=\frac{c \mu_{0} b} {\pi} H_{\mathrm{o}}=5. 9 8 \times10^{4} \mathrm{~ V / m}
$$
$$
\left. \mid\dot{H}_{x} \mid_{\mathrm{m a x}}=\frac{\beta a H_{0}} {\pi} \mathrm{s i n} \left( \frac{\pi x} {a} \right) \right|_{z=b / 2}=\frac{3 b} {\lambda_{1}} H_{0}=9 5. 1 5 \quad\mathrm{A / m}
$$
$$
| \ \dot{H}_{z} \ |_{\mathrm{m a x}}=\left| H_{\circ} \mathrm{c o s} \Big( \frac{\pi x} {b} \Big) \right| |_{x=0, \, \pi}=H_{0}=1 2 6. \, 8 7 \quad\mathrm{A / m}
$$
C. $$
\vert\ \dot{E}_{y} \vert_{\mathrm{m a x}}=\eta_{0} \Big( \frac{2 a} {\lambda_{0}} \Big) H_{\mathrm{o}}=\frac{a \mu_{0} a} {\pi} H_{\mathrm{o}}=5. 9 8 \times1 0^{4} \mathrm{~ V / m}
$$
$$
\left. \mid\dot{H}_{x} \mid_{\mathrm{m a x}}=\frac{\beta a H_{0}} {\pi} \mathrm{s i n} \left( \frac{\pi x} {a} \right) \right|_{z=a / 2}=\frac{2 a} {\lambda_{1}} H_{0}=9 5. 1 5 \quad\mathrm{A / m}
$$
$$
| \ \dot{H}_{z} \ |_{\mathrm{m a x}}=\left| H_{\circ} \mathrm{c o s} \Big( \frac{\pi x} {a} \Big) \right| |_{x=0, \, \pi}=H_{0}=1 2 6. \, 8 7 \quad\mathrm{A / m}
$$
D. $$
\vert\ \dot{E}_{y} \vert_{\mathrm{m a x}}=\eta_{0} \Big( \frac{6 a} {\lambda_{0}} \Big) H_{\mathrm{o}}=\frac{c \mu_{0} c} {\pi} H_{\mathrm{o}}=5. 9 8 \times10^{4} \mathrm{~ V / m}
$$
$$
\left. \mid\dot{H}_{x} \mid_{\mathrm{m a x}}=\frac{\beta a H_{0}} {\pi} \mathrm{s i n} \left( \frac{\pi x} {a} \right) \right|_{z=c / 2}=\frac{6 a} {\lambda_{1}} H_{0}=9 5. 1 5 \quad\mathrm{A / m}
$$
$$
| \ \dot{H}_{z} \ |_{\mathrm{m a x}}=\left| H_{\circ} \mathrm{c o s} \Big( \frac{\pi x} {a} \Big) \right| |_{x=0, \, \pi}=H_{0}=1 2 6. \, 8 7 \quad\mathrm{A / m}
$$
E. $$
\vert\ \dot{E}_{y} \vert_{\mathrm{m a x}}=\eta_{0} \Big( \frac{2 a} {\lambda_{1}} \Big) H_{\mathrm{o}}=\frac{b \mu_{0} a} {\pi} H_{\mathrm{o}}=5. 9 8 \times10^{4} \mathrm{~ V / m}
$$
$$
\left. \mid\dot{H}_{x} \mid_{\mathrm{m a x}}=\frac{\beta c H_{0}} {\pi} \mathrm{s i n} \left( \frac{\pi x} {c} \right) \right|_{z=a / 2}=\frac{3 a} {\lambda_{0}} H_{0}=9 5. 1 5 \quad\mathrm{A / m}
$$
$$
| \ \dot{H}_{z} \ |_{\mathrm{m a x}}=\left| H_{\circ} \mathrm{c o s} \Big( \frac{\pi x} {c} \Big) \right| |_{x=0, \, \pi}=H_{0}=1 2 6. \, 8 7 \quad\mathrm{A / m}
$$
F. $$
\vert\ \dot{E}_{y} \vert_{\mathrm{m a x}}=\eta_{0} \Big( \frac{4 a} {\lambda_{0}} \Big) H_{\mathrm{o}}=\frac{a \mu_{0} b} {\pi} H_{\mathrm{o}}=5. 9 8 \times10^{4} \mathrm{~ V / m}
$$
$$
\left. \mid\dot{H}_{x} \mid_{\mathrm{m a x}}=\frac{\beta a H_{0}} {\pi} \mathrm{s i n} \left( \frac{\pi x} {a} \right) \right|_{z=a / 2}=\frac{4 a} {\lambda_{1}} H_{0}=9 5. 1 5 \quad\mathrm{A / m}
$$
$$
| \ \dot{H}_{z} \ |_{\mathrm{m a x}}=\left| H_{\circ} \mathrm{c o s} \Big( \frac{\pi x} {a} \Big) \right| |_{x=0, \, \pi}=H_{0}=1 2 6. \, 8 7 \quad\mathrm{A / m}
$$
G. $$
\vert\ \dot{E}_{y} \vert_{\mathrm{m a x}}=\eta_{0} \Big( \frac{2 c} {\lambda_{0}} \Big) H_{\mathrm{o}}=\frac{c \mu_{0} a} {\pi} H_{\mathrm{o}}=5. 9 8 \times10^{4} \mathrm{~ V / m}
$$
$$
\left. \mid\dot{H}_{x} \mid_{\mathrm{m a x}}=\frac{\beta c H_{0}} {\pi} \mathrm{s i n} \left( \frac{\pi x} {c} \right) \right|_{z=c / 2}=\frac{2 c} {\lambda_{1}} H_{0}=9 5. 1 5 \quad\mathrm{A / m}
$$
$$
| \ \dot{H}_{z} \ |_{\mathrm{m a x}}=\left| H_{\circ} \mathrm{c o s} \Big( \frac{\pi x} {c} \Big) \right| |_{x=0, \, \pi}=H_{0}=1 2 6.\, 8 7 \quad\mathrm{A / m}
$$
H. $$
\vert\ \dot{E}_{y} \vert_{\mathrm{m a x}}=\eta_{0} \Big( \frac{4 c} {\lambda_{0}} \Big) H_{\mathrm{o}}=\frac{a \mu_{0} a} {\pi} H_{\mathrm{o}}=5. 9 8 \times10^{4} \mathrm{~ V / m}
$$
$$
\left. \mid\dot{H}_{x} \mid_{\mathrm{m a x}}=\frac{\beta c H_{0}} {\pi} \mathrm{s i n} \left( \frac{\pi x} {c} \right) \right|_{z=c / 2}=\frac{4 c} {\lambda_{1}} H_{0}=9 5. 1 5 \quad\mathrm{A / m}
$$
$$
| \ \dot{H}_{z} \ |_{\mathrm{m a x}}=\left| H_{\circ} \mathrm{c o s} \Big( \frac{\pi x} {c} \Big) \right| |_{x=0, \, \pi}=H_{0}=1 2 6. \, 8 7 \quad\mathrm{A / m}
$$
I. $$
\vert\ \dot{E}_{y} \vert_{\mathrm{m a x}}=\eta_{0} \Big( \frac{3 a} {\lambda_{0}} \Big) H_{\mathrm{o}}=\frac{b \mu_{0} a} {\pi} H_{\mathrm{o}}=5. 9 8 \times10^{4} \mathrm{~ V / m}
$$
$$
\left. \mid\dot{H}_{x} \mid_{\mathrm{m a x}}=\frac{\beta b H_{0}} {\pi} \mathrm{s i n} \left( \frac{\pi x} {b} \right) \right|_{z=b / 2}=\frac{3 a} {\lambda_{1}} H_{0}=9 5. 1 5 \quad\mathrm{A / m}
$$
$$
| \ \dot{H}_{z} \ |_{\mathrm{m a x}}=\left| H_{\circ} \mathrm{c o s} \Big( \frac{\pi x} {b} \Big) \right| |_{x=0, \, \pi}=H_{0}=1 2 6. \, 8 7 \quad\mathrm{A / m}
$$
J. $$
\vert\ \dot{E}_{y} \vert_{\mathrm{m a x}}=\eta_{0} \Big( \frac{5 a} {\lambda_{0}} \Big) H_{\mathrm{o}}=\frac{b \mu_{0} c} {\pi} H_{\mathrm{o}}=5. 9 8 \times10^{4} \mathrm{~ V / m}
$$
$$
\left. \mid\dot{H}_{x} \mid_{\mathrm{m a x}}=\frac{\beta b H_{0}} {\pi} \mathrm{s i n} \left( \frac{\pi x} {b} \right) \right|_{z=b / 2}=\frac{5 a} {\lambda_{1}} H_{0}=9 5. 1 5 \quad\mathrm{A / m}
$$
$$
| \ \dot{H}_{z} \ |_{\mathrm{m a x}}=\left| H_{\circ} \mathrm{c o s} \Big( \frac{\pi x} {b} \Big) \right| |_{x=0, \, \pi}=H_{0}=1 2 6. \, 8 7 \quad\mathrm{A / m}
$$
Answer: C