A plane electromagenic wave having a frequency `v= 23.9 GHz` propagates along the positive z-direction in free space. The peak value of the Electric field is `60 V//m` Which among the following is the acceptable magnetic field component in the electromagnetic wave ?

Options

A. `vec(B) = 60 sin (0.5 xx 10^(3) x + 1.5 xx 10 ^(11) t) hat(k)`
B. `vec(B) = 2 xx 10 ^(-7) sin (0.5 xx 10^(3) z - 1.5 xx 10 ^(11) t) hat(i)`
C. `vec(B) = 2 xx 10^(7) sin (0.5 xx 10^(3) z + 1.5 xx 10 ^(11) t) hat(i)`
D. `vec(B) = 2 xx 10^(-7) sin (1.5 xx 10^(2) x + 0.5 xx 10 ^(11) t) hat(j)`

Answer

B

Explanation

`B_(0) = (E_(0))/( c) = 2 xx 10^(-7)`
`K = (omega)/(c) = (2 pi t)/( c) = 0.5 xx 10 ^(3)`
`omega = 2 pi f = 1.5 xx 10 ^(11) and B = b_(0) sin ( k z pm omega t ) hat(i)`