Why Does E=mc2_ - Brian Cox [12]
What are these mysterious oscillating fields? Imagine an electric field beginning to grow because Faraday generates a pulse of electric current in a wire. We have already learned that as the pulse of electric current passes along the wire, a magnetic field is generated (remember that Faraday observed that a compass needle in the vicinity of the wire is deflected). In Maxwell’s language, the changing electric field generates a changing magnetic field. Faraday also tells us that when we change a magnetic field by pushing a magnet through a coil of wire, an electric field is generated, which causes a current to flow in the wire. Maxwell would say that a changing magnetic field generates a changing electric field. Now imagine removing the currents and the magnets. We are left with just the fields themselves, swinging backward and forward as changes in one generate changes in the other. Maxwell’s wave equations describe how these two fields are linked together, oscillating backward and forward. They also predict that these waves must move forward with a particular speed. Perhaps not surprisingly, this speed is fixed by the quantities Faraday measured. In the case of sound waves, the wave speed is approximately 330 meters per second, just a little bit faster than a passenger airplane. The speed of sound is fixed by the details of the interactions between the air molecules that carry the wave. It changes with varying atmospheric pressure and temperature, which in turn describe how closely the air molecules get to each other and how fast they bounce off each other. In the case of Maxwell’s waves, the speed is predicted to be equal to the ratio of the strengths of the electric and magnetic fields, and this ratio can be measured very easily. The strength of the magnetic field can be determined by measuring the force between two magnets. The word “force” will crop up from time to time, and by it we mean the amount by which something is pushed or pulled. The amount of push/pull can be quantified and measured, and if we are trying to understand how the world works, it should come as little surprise that we will want to understand how forces originate. In an equally simple way, the electric field strength can be measured by charging up two objects and measuring the force between them. You may have inadvertently experienced that “charging up” process yourself. Perhaps you’ve walked around over a nylon carpet on a dry day and then received an electric shock when you tried to open a door with a metal handle. This unpleasant door-opening experience occurs because you have rubbed electrons, the fundamental particles of electricity, off the carpet and into the soles of your shoes. You have become electrically charged, and this means that an electric field exists between you and the door handle. Given the chance when you grab hold of the door handle, this field will cause an electric current to flow, just as Faraday found in his experiments.
By carrying out such simple experiments, scientists can measure the strengths of the electric and magnetic fields, and Maxwell’s equations predict that the ratio of strengths gives the speed of the waves. What, then, is the answer? What did Faraday’s benchtop measurements, coupled with Maxwell’s mathematical genius, predict for the speed of the electromagnetic waves? This is one of many key moments in our story. It is a wonderful example of why physics is a beautiful, powerful, and profound subject: Maxwell’s waves travel at 299,792,458 meters per second. Astonishingly, this is the speed of light—Maxwell had stumbled across an explanation of light itself. You see the world around you because Maxwell’s electromagnetic field drives itself through the darkness and into your eyes, at a speed predictable using only a coil of wire and a magnet. Maxwell’s equations are the crack in