In a region of free space, the elctric field at some instant of time is, `E = (80hati + 32hatj - 64hatk) Vm^(-1)` and the magnetic field is `B = (0.2hati + 0.08hatj + 0.29jhatk)muT`.
(i) Show that these two fields are perpendicular to each other.
(ii) Determine the poynting vector for these fields.

Explanation

(i) E will be perpendicular to B, if `E.B = 0`
Now,
`E.B = (80hati + 32hatj -64hatk).(0.2hati + 0.08hatj + 0.29hatk)`
`= (80 xx 0.2 + 32 xx 0.08 - 64 xx 0.29) = 0`
Thus, we can say that `E _|B`.
(ii) Thus poything vector, `S = (1)/(mu_(0)) (E xx B)`
`= (1)/(4pi xx 10^(-7)) |{:(hati,hatj,hatk),(80,32,-64),(0.2,0.08,0.29):}|`
`= [11.52hati - 28.8hatj] xx 10^(6)Wm^(-2)`