If the magnetic field of a plane electromagnetic wave is given by `5xx10^(-6) sin (0.6 xx 10^2 x + 0.5 xx 10^(10) t)`, then the speed of the wave is

Options

A. `0.83 xx 10^7` m/s
B. `0.83 xx 10^8` m/s
C. `5.24 xx 10^8` m/s
D. `5.24 xx 10^9` m/s

Answer

B

Explanation

Given expression `= 5xx 10^(-6) sin (0.6 xx 10^2 x + 0.5 xx 10^10)" "…(1)`
Compare equation (1) with,
`B_y = B_(0) sin (2pi ((x)/(lambda) + (t)/(T )))`
`= 5 xx 10^(-6) [sin 2pi ( (0.6 xx 10^2 )/(2pi)) x+ ((0.5 xx 10^10)/(2 pi ))t ]`
`(1)/(lambda) = (0.6 xx 10^2 )/( 2pi ) = 9.549`
`therefore` Wavelength `lambda = 0.1047`
Frequency `= (1)/(T) = (0.5 xx 10^(10))/(2 pi)`
`therefore f = 299. 4 xx 10^6`
Speed = Wavelength * Frequency
`= 83. 3 xx 10^6`
`therefore` Speed ` = 0.83 xx 10^8 ` m/sec