A plane e.m. wave propagating in the x-direction has a wavelength `6.0 mm`. The electric field is in the y-direction and its maximum magitude is `33Vm^_1`. Write suitable equation for the electric and magnetic fields as a function of `x` and `t`.

Explanation

Here, `lambda = 6 xx 10^(-3) m, " " E_(0) = 33 `V/m
`omega = 2pi v = (2pi c )/(lambda) = (2 pi xx 3 xx 10^(8))/(6 xx 10^(-3)) = pi xx 10^(11) `rad/s.
The maximum magnetic field.
`B_(0) = (E_(0))/(c ) = (33)/(3 xx 10^(8)) = 11 xx 10^(-8) `T
As wave propagates along x -axis, so electric field should be along y-axis and magnetic field along Z-axis, so that `vec(E) bot vec(B) bot vec(C ) ` is satisfied.
the equation for the electric field, along y-axis in the electromagnetic wave is
`E_(y) = E_(0)sin omega(t (x)/(c ) ) ` = 33 sin` pi xx 10^(11) `(t - x/c)
The equation for the magnetic field along z-axis in the electromagnetic wave is
`B_(z) = B_(0) sin omega(t (x)/(c)) = 11 xx 10^(-8) sin pi xx 10^(11) `(t - x/c)