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

Given:
Magnetic frequency of e.m. wave, `lambda = 10^(10)` Hz
Amplitude of e.m. wave `A_(0) = 10^(-5)` T
To find :
Wavelength of e.m. wave, `lambda` = ?
`lambda = (c )/(gamma) = ("velocity of light in vacuum")/("frequency of e.m. wave") = (3 xx 10^(8))/(10^(10))`
`lambda = 3 xx 10^(-2) `m.
Amplitude of electric field `E_(0)` = ?
`B_(0) = (E_(0))/(C ) rArr E_(0) = B_(0)cdot C`
`E_(0) = 10^(-5) xx 3 xx 10^(8) = 3 xx 10^(3)`
`E_(0) = 3 xx 10^(3)" V" m^(-1) `(or) N `C^(-1)`
Formula
the expression for electric field is
`E = E_(0) sin ( kx - omega t)`
Where k = `(omega)/(c ) , omega = 2pi lambda`
`= 2 xx 3.14 xx 10^(10) = 6.28 xx 10^(10)`
` k = (2pi gamma)/(c ) = (6.28 xx 10^(10))/(3 xx 10^(8)) = 2.09 xx 10^(2)`
subtraction in (1)
the wave is propergating along x - axis and
magnetic field oscillates `(vec(B))` along y - axis, E will be
`vec(E) = 3 xx 10^(3) sin (2.09 xx 10^(2) x - 6.28 xx 10^(10) t) hat(i) NC^(-1)`