The magnetic field in a plane electromagnetic wave is given by `B_(y) = 2xx10^7 T sin (0.5xx10^3x+1.5xx10^11 t) T`
(a) What is the wavelength and frequency of the wave?
(b) Write an expression for the eletric field.

Explanation

Given
By `= 2 x10^(–7) sin (0.5 x10^(3)x + 1.5 x10^(11))`
(a) Comparing it with a standard equation for a progressive wave travelling along the negative direction of x-axis is
`y= r sin (2pi)/lambda (x + vt)`
` = r sin ((2pix)/lambda + (2pivt)/lambda)`
` = r sin ((2pix)/lambda + 2pivt)`
We have, `(2pix)/lambda = 0.5 xx 10^(3) x`
or `lambda = (2pi)/(0.5xx10^(3))=12.56xx10^(-3)x`
`=12.56`mm
`2piv = 1.5 xx 10^(11)`
`v= (1.5xx10^(11))/(2pi)`
`= 23.9 x10^(9) Hz = 23.9 `Hz
(b)` E_(0) = cB_(0) = (3 x10^(8)) ×(2 x10^(–7)) `
`= 60 Vm^(-1)`
`therefore E_(z) = E_(0) sin (2pi)/lambda (x+ vt)`
`= E_(0) sin ((2pix)/lambda + (2pit)/lambda)`
or ` E_(z) = 60 sin (0.5xx 10^(3) x + 1.5 xx 10^(11)t)`V/m