A plane e.m. wave travelling along the x-direction has a wavelength of 3mm. The variation in the electric field occurs in the y-direction with an amplitude `66Vm^-1`. The equation for the electric and magnetic fields as a function of x and t are respectively

Options

A. `E_(y) = 33 cos pi xx 10^(11) (t- x/c), B_(y) = 1.1 xx 10^(-7) cos pi xx 10^(11) (t-x/c)`
B. `E_(y) = 11 cos 2pi xx 10^(11) (t-x/c), B_(y) = 11 xx 10^(-7) cos 2pi xx 10^(11) (t-x/c)`
C. `E_(X) = 33 cos pi xx 10^(11)(t-x/c), B_(X) = 11 xx 10^(-7) cos pi xx 10^(11) (t- x/c)`
D. `E_(Y) = 66 cos 2 pi xx 10^(11) (t-x/c), B_(Z) = 2.2 xx 10^(-7) cos 2pi xx 10^(11)(t-x/c)`

Answer

D

Explanation

The equation of electric field occuring in Y-direction.
`E_(Y) = 66 cos 2pi xx 10^(11)(t-x/c)`
Therefore, for the magnetic field in Z-direction.
`B_(Z) = E_(Y)/c = 66/(3 xx 10^(8)) cos 2pi xx 10^(11) (t-x/c)`
`=22 xx 10^(-8) cos 2pi xx 10^(11) (t-x/c)`
`=2.2 xx 10^(-7) cos 2pi xx 10^(11) (t-x/c)`