Poynting Vector

New for December 2021. We've added some description of Poynting's vector, and a cool video that explains the concept. The Poynting vector is used in EM analysis, and is named after British physicist John Henry Poynting. We've put him in the Microwaves101 Hall of Fame.

Poynting's vector represents the directional energy flux or power flow of an electromagnetic field, in Watts/meter^2. It's a huge coincidence that the Poynting vector is "pointing" in the direction of energy flow.

The Poynting vector is generally denoted S, and is the vector cross-product (or "curl") of E and H fields:


By the way, here is another website's discussion on when to decorate vector notations. Out of laziness, we are not even going to look up how to add the little arrows...

The cool thing about the Poynting vector is if you can quantify magnetic and electric flux magnitudes and directions, you can tell which direction energy is flowing. The vector cross products always follow a "right-hand rule". When you point your right-hand fingers in the direction of the E-field, and curl them toward the H-field, your right hand thumb points in the direction of propagation.  If you applied it to a power line, you would know which direction the power company was, for example.

Here's a great discussion of how to apply the right-hand rule to vector cross-products, by BraunVideos.

Right-hand rule for vector cross-product, by BraunVideos

This website has a nice image of E and H fields in TEM mode. Take a look, apply the right-hand rule and you will see that the generator is on the left and the load is on the right. One of these days we'll make some images of our own to illustrate Poynting's vector.

Here's a true story, maybe some other engineers experienced this: sitting in an electromagnetics exam in college, there is a question about which direction energy is flowing. More than one right-handed person gets it wrong, as they are holding a pencil in their right hand, while doing the cross-product with their left hand.... Doh!

Below is a video that dispels the notion that electrons carry energy around a complete conducting loop, transferring their energy to the load. In most cases, you can pretend this is happening, but reality is stranger (hint: it can all be explained by the Poynting vector.) This video is from the "Veritasium" YouTube channel, which also has some other great physics-related discussions.  Our only comment on the video is when he explains the cross-product the first time, he doesn't mention right-handed-ness. He makes that distinction later though.

The Big Misconception About Electricity by Veritasium

Thanks to David S. for suggesting we look at this video!