A plane electromagnetic wave travels in free space along X-direction. If the value of `vecB` (in tesla) at a particular point in space and time is `1.2 xx 10^(-8) hatk`. The value of `vecE` (in `Vm^(-1)`) at that point is

Options

A. `1.2hatj`
B. `3.6hatk`
C. `1.2hatk`
D. `3.6hatj`

Answer

D

Explanation

Here, `vec(B)=1.2xx110^(-8)hatkT`
The magnitude of `vecE` is
`E=Bc=(1.2xx10^(-8)T)(3xx10^(8)"m s"^(-1))=3.6"V m"^(-1)`
`vec(B)` is along Z-direction and the wave propagates along X-direction. Therefore `vecE` should be in a direction perpendicular to both X and Z axes. Using vector algebra `vec(E)xxvec(B)` should be along X-direction.
Since `(+hatj)xx(+hatk)+hati,vecE` is along the Y-direction.
Thus, `vecE=3.6hatj"V m"^(-1)`.