The magnetic field in a plane electromagnetic wave is given by `B_(y)=(2xx10^(-7)) T sin (0.5xx10^(3)x+1.5xx10^(11)t)`.
Write an expression for the electric field.

Explanation

If amplitudes of oscillations of electric and magnetic field are respectively `E_(0)` and `B_(0)`, then
`c=(E_(0))/(B_(0))`
`therefore E_(0)=B_(0)c`
`=(2xx10^(-7))(3xx10^(8))` [From equ. (2)]
`therefore E_(0)=60 Vm^(-1)`
Here `vec(B)` oscillates along Y - axis and electromagnetic wave propagates along X - axis. Hence `vec(E )` must be oscillating on Z - axis and so its equation will be,
`E=E_(z)=E_(0)sin(kx + omega t)`
`therefore E_(z)=60 sin{(0.5xx10^(3))x+(1.5xx10^(11))t}Vm^(-1)`
Vectorially,
`vec(E )=60 sin {(0.5xx10^(3))x + (1.5xx10^(11))t} hat(k) Vm^(-1)`