Cancellation of Poynting vector components

[Karthiksrao]

If we find the Poynting vector at a point along all possible directions possible, can the different components of the vectors cancel each other, to give a net Poynting vector along some direction?

I was wondering about this because Poynting vector after all represents energy flow. So can energy flow along different directions cancel each other ?

I suppose we can, since energy and momentum are interrelated and I can imagine momentum components canceling. I just wanted to confirm if my thought process is correct.

Thanks

 

[chrisbaird]

The question can be very misleading as stated. What I think you mean to ask is: Can the Poynting vector from one system cancel the Poynting vector from another system? (Components of a single vector cannot cancel because components are by definition independent.)

The answer is yes. If you have a source emitting an EM wave through a certain space and another source emitting another EM wave through the same space at the same frequency, but in the opposite direction, you get a standing wave. A standing wave does not travel or carry energy, so its average Poynting vector is zero. You can think of it as the Poynting vector of the one wave canceling the other. Although you have to be careful to differentiate between instantaneous Poynting vector and time-averaged. And if there is a coherent interaction of the waves, you have to sum fields, and not intensities.

 

[Karthiksrao]

Thanks for the answer.