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What are fields?

What are gravitational fields? Electric fields? Magnetic fields? the electromagnetic field?

What do physicists mean by the term “field”?

Imagine our universe is flat. We could describe what’s going on at any point by defining a 2D grid, like graph paper.

2-d field representing temperature

2-d field representing wind speed

windspeed

Our universe is 3D. We need 3 dimensions – 3 axes – to describe any point in space.

This image shows an empty universe, with nothing in it.

Imagine this 3D grid extending through our world:

(indoor 3D climbing array by Croatian-Austrian artists  Sven Jonke, Christoph Katzler and Nikola Radeljković.)

Is our world filled with actual fields? Yes.

Our universe is filled with an electromagnetic field which allows magnetism to exist.

Consider a horseshoe magnet – it’s a 3D object, with a 3D magnetic field invisibly emanating from it. How can we visualize this invisible field? How about tossing in a few thousand small iron filings! 🙂

What’s special about the electromagnetic field? It isn’t really being created by the magnet – it is already everywhere. In us, around us, throughout the entire universe.

At every single point in our universe appears to be a vector electric field (has both magnitude and intensity), and a vector magnetic field. In fact, it turns out that there is really just one field – the electromagnetic field – that exists throughout our universe. And as particles move and interact with each other, the quantities at each point in this field change.

(image of magnetic field by cordelia molloy )

So imagine that each point in space – even the one right at your index finger’s tip, already has a value for an electromagnetic field. Maybe the value, at this moment, for both E and B is small, maybe even zero – but it still has a value.

As a magnet moves close to you, the values at each point in this field change. We can’t see it with our eyes or feel it with our fingers – but we can measure it by seeing the effect it has on a compass – or the effect it has on the magnetometer built into your cell phone (and yes, there’s an App for that!)

Physics Toolbox Magnetometer: google play

 

“Nickolay Lamm has already made the invisible visible with a project that showed what Wi-Fi would look like if we could see it, but for his latest series of images, the artist has turned his attention to cell phones. Cell phone networks across the country are made up of multiple hexagonal areas, each of which is called a cell, that you can clearly make out in the images. The hexagonal grid is efficient, as each cell tower sits at the intersection of three cells, and each of the three directional antennas on top of the tower covers a 120-degree slice of the landscape.”

“To make sure his illustrations were as accurate as possible, Lamm worked with two professors of electrical and computer engineering: Danilo Erricolo at the University of Illinois at Chicago and Fran Harackiewicz at Southern Illinois University in Carbondale.”

What if you had an app on a tablet that let you (roughly) visualize a part of the EM field in this very room?

To be clear, no single device can measure every part of the EM field. One would need different sensors to record each part of it. Even when many parts are recorded, there is no useful way to show all of it at once: you’d be piling multiple images on top of each other, leading to a dense, impossible-to-see mess. But you can use a device to measure any one of these, and then display this data on its own:

The EM field can include:

  • radio waves / WiFi signals

  • microwaves

  • infrared

  • visible light

  • ultraviolet

An app created by Richard Vijgen, called Architecture of Radio, visualizes the overlapping signals that envelop us — from cell towers, WiFi routers, and even satellites flying overhead.  The app, at the moment, is site-specific to an installation in Germany. It uses GPS to get the user’s location then finds nearby cell towers using OpenCellID, and has been custom-programmed to map the WiFi routers and Ethernet cables in the exhibition space. It also uses OpenCellID to predict any satellites that might pass overhead. The app then uses this data to visualize the signals swirling around the exhibition-goers, showing what the project’s website refers to as the “infosphere” that we all live in now.

This app lets you visualize the WiFi signals pulsing around you

Now understand that our entire universe is filled with such fields:

AP Physics Learning Objectives

Essential Knowledge 2.A.1: A vector field gives, as a function of position (and perhaps time), the value of a physical quantity that is described by a vector.

a. Vector fields are represented by field vectors indicating direction and magnitude.
b. When more than one source object with mass or electric charge is present, the field value can be determined by vector addition.
c. Conversely, a known vector field can be used to make inferences about the number, relative size, and location of sources.

Content Connection: This essential knowledge does not produce a specific learning objective but serves as a foundation for other learning objectives in the course.

Essential Knowledge 2.A.2: A scalar field gives, as a function of position (and perhaps time), the value of a physical quantity that is described by a scalar. In Physics 2, this should include electric potential.
a. Scalar fields are represented by field values.
b. When more than one source object with mass or charge is present, the scalar field value can be determined by scalar addition.
c. Conversely, a known scalar field can be used to make inferences about the number, relative size, and location of sources.

Content Connection: This essential knowledge does not produce a specific learning objective but serves as a foundation for other learning objectives in the course.

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