Let an electromagnetic wave propagate along the x direction, the magnetic field oscillates at a frequency of ` 10^(10) ` Hz and has an amplitude of ` 10 ^(-5) T`, acting along the y - direction. Then, compute the wavelength of the wave. Also write down the expression for electric field in this case.

Explanation

Electric field
` E _ s = E_0 sin [ Kx - omega t ] `
` E_x = E_0 sin [ (2pi)/(lamda ) x - 2pi f t ]`
`{:(C = (E_0)/(B_0)),( therefore E_0 = CB_0),(E_0 = 3 xx 10^(8) xx 10 ^(-5)),(E_0 = 3 xx 10^3):}:|{:( lamda = (C)/(f) = (3xx 10^8)/(10^(10))),(lamda =3 xx10^(-2) m),( (2pi)/(lamda) =(2 xx 3.14)/(3) xx 10^(+2)),(rArr (2pi)/(lamda) = (6.28)/(3) xx 10 ^(2)),((2pi)/(lamda) = 2.09 xx 10^2):}`
` 2pi f = 2 xx 3.14 xx 10 ^(10) `
` 2 pi f = 6.28 xx 10^(10)`
` therefore E _ x = 3 xx 10 ^(3) [ sin (2.09 xx 10 ^2 x - 6.28 xx 10 ^(10) t ) ] NC^(-1) `