A plane electromagnetic wave of frequency 50 MHz travels in free space along the x-direction. At a particular point in space and time, `vecE=6.3hatj"V m"^(-1)`.
At this point `vecB` is equal to

Explanation

The magnitude of `hatB` is
`B=(E )/(C )=(6.3 V//m)/(3xx10^(8)m//s)=2.1 xx10^(-8)T`
To find the direction, we note that E is along y-direction and the wave propagates along x-axis. Therefore, B should be in a direction perpendicular to both x-and y-axes. Using vector algebra, E x B should be along x-direction. Since, `(+hatj) xx (+hatk) = hati B` is along the z- direction. Thus, `B = 2.1xx 10^(-8) hatk T`