Problem 16.7

ĉîĵ

กำหนดให้ \(= , E_{\max}= 750 N/C, f = 40.0 MHz, \vec{E}(0,0) = E_{\max}\)

a)จาก\(T=\frac{1}{f}=25.0ns\;\blacksquare\)

b) จาก \(c = fλ\)

\(\lambda =\frac{c}{f}=7.50m\;\blacksquare\)

c) จาก \(k = \frac{2\pi}{\lambda}= 0.838 rad/m\)

จาก \(ω = 2πf = 2.51\times 10^{9} rad/s\)

จาก \(E(x,t) = E_{\max}\cos (kx - \omega t + φ)\)

ĵ

\(\vec{E}(x,t) = E_{\max}\cos (kx - \omega t + φ)\)

ĵĵ

\(E_{\max}= E_{\max}\cos (k(0) - \omega (0) + φ)\)

\(1 = \cos (φ)\)

\(φ = 0 rad\)

ĵ

\(\therefore \vec{E}(x,t) = (750 N/C)\cos ((0.838 rad/m)x - (2.51\times 10^{9} rad/s)t) \;\blacksquare\)

d) จาก \(c = \frac{E_{\max}}{B_{\max}}\)

\(B_{\max}=\frac{E_{\max}}{c}= 2.50 \mu T\)

ĉÊ B̂

จาก \(= \times \)

îĵ B̂

\(= \times\)

B̂k̂

\(\therefore =\)

จาก \(B(x,t) = B_{\max}\cos (kx - \omega t + φ)\)

k̂

\(\therefore \vec{B}(x,t) = (2.50 \mu T)\cos ((0.838 rad/m)x - (2.51\times 10^{9} rad/s)t) \;\blacksquare\)