A plane electromagnetic sinusoidal wave of frequency 51.1 MHz travels in free sp

Question

A plane electromagnetic sinusoidal wave of frequency 51.1 MHz travels in free space.
The speed of light is 2.99792 × 108 m/s.

1) Determine the wavelength of the wave.
Answer in units of m. Answer must be to 6 significant digits!

2) Find the period of the wave.
Answer in units of s. Answer must be to 6 significant digits!

3) At some point and some instant, the electric field has has a value of 658 N/C. Calculate the magnitude of the magnetic field at this point and this instant.
Answer in units of T. Answer must be to 6 significant digits!

Explanation / Answer

1)  Given     frequency of electromagnetic wave  f  =  51.1 *106  Hz     speed of  light   v =   2.99792 * 10 8  m/s      wave length of the wave                    =  c  / f                     =  2.99792 *10 8   /  51.1 *10 6                        = 5.8667710 m  2)    time period  of the wave                T  = 1  / f                    =  1  /  51.1 *10 6                        = 1.956947*10-8  s    3) given  magnitude  of electric field     E  = 658 N /C   the  relation between electric field  and  magnetic field                E  / B   =  c      magnitude  of  magnetic field                B  =   E  / c                    =  658 N  /C  / ( 2.99792 * 10 8  m/s )                    = 2.1948550*10-6 T  

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