Em Waves Question 132
Question: Which of the following is the correct equation for magnetic field as a function of x, and t where a plane electromagnetic wave propagating in the x-direction has a wavelength of 5.0 mm? The electric field is in the y-direction and its maximum value is $ 30,V{{m}^{-1}} $ .
Options:
A) $ B={{10}^{-3}},\sin ,[ \frac{2\pi }{5\times {{10}^{-3}}}(ct-x) ] $
B) $ B={{10}^{-7}},\sin ,[ \frac{2\pi }{5\times {{10}^{-3}}}(ct-x) ] $
C) $ B={{10}^{-5}},\sin ,[ \frac{\pi }{1.5\times {{10}^{-3}}}(ct-x) ] $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ E=E _{0}\sin ,\omega ( t-\frac{x}{c} ) $ ; $ B=B _{0}\sin \omega ( t-\frac{x}{c} ) $
$ I _{d}=I _{0}\sin ( \omega t+\frac{\pi }{2} )=I $ and $ \omega =2\pi v=\frac{2\pi }{\lambda }c $
$ E _{0}=30\sin [ \frac{2\pi }{5\times {{10}^{-3}}}(ct-x) ] $ and $ B _{0}=\frac{E _{0}}{C}={{10}^{-7}}T $
$ B=B _{0}\sin [ \frac{2\pi }{\lambda }(ct-x) ]={{10}^{-7}}\sin [ \frac{2\pi }{5\times {{10}^{-3}}}(ct-x) ] $
BETA
