# Why do magnetic fields appear when an electric current passes through a wire?

1. Jun 14, 2012

### cheah10

I've checked Wikipedia for answers but can't find any. I'm learning electromagnetism in school now. I don't know why this happens and so I can't understand the lessons! Can anyone tell me why? Thx :)

2. Jun 14, 2012

### vanhees71

Physics or any Natural Science can't explain you why things are as they are. As a physicist you only try to describe what happens as accurately as you can. For that purpose you make observations in nature or prepare an experiment in the lab to control all circumstances of a well-defined setup as well as you can. Such observations are made quantitative by defining units for certain observables like length, time, mass, electric charges, currents, and so on.

In the history of modern science, particularly in physics which deals with the most fundamental properties of phenomena, it however turned out that one observes quite regular patterns that can be summarized into fundamental natural laws, which can described mathematically in theories or at least models of certain aspects of the behavior of matter.

The first theory of this kind has been the development of classical mechanics by Newton in the 17th century. From a very few basic principles this theory describes a lot of phenomena from the everyday motion of bodies around us to the planetary motion within our solar system. It also can provide you with ideas, how to use these fundamental laws to build machines or it helps you to plan how to fly to the moon or how to set out a satellite for broadcasting or meteorology etc. etc.

In this sense, "why" questions like yours can be answered by natural sciences in a very specific way, namely to tell you what are the so far known basic principles underlying the phenomenon you are after.

In your case it's the question, "why" magnetic fields appear when you have a current-conducting wire around. The answer of this question, to the best of our knowledge today, in the above sense, is that it is a fundamental law of electromagnetism, which can be described by a theory called "classical electrodynamics", that has been found by Maxwell in the mid of the 19th century and his successors. It's, however, the result of a century-long process of observations concerning electricity and magnetism, going to experiments, making models to summarize the observations finally into a theory which describes as large an amount of observational facts as you can with the least possible mathematical effort and assumptions.

In the beginning (at least with the ancient greeks) electricity and magnetism have been described only qualitatively and nobody has had any clue about their close connection. Later on, after Newton's big success with the mathematical description of mechanical phenomena (and by the way inventing a then completely new kind of mathematics, nowadays called calculus (differentiation and integration) and analytical (differential) geometry (vector calculus)) of course many people started to think about the electric forces and the magnetic forces and made models very similar to Newton's principle law governing the gravitational force which described so different things as a falling apple and the revolution of the Moon around the Earth.

Then, at some time in the early 19th century, by chance Oersted observed that around a current-conducting wire compass needles are moving similar to the same effect caused by a permanent magnet of the Earth's magnetic field. Nobody had any idea before, how closely related electricity and magnetism in fact are. Then again other physicists like Weber and Ampere made models to describe this phenomenon, and the models in turn have been checked with experiments, etc. etc.

Then Faraday, one of the most brillant experimental physicists of all time, came up with a new idea to describe electromagnetic phenomena, namely the idea that there are not actions at a distance or instaneous forces caused by electric charges and currents but that these "sources" are causes for electric and magnetic fields, and that these in turn are the cause of the forces of charged or magnetized bodies at their position in this field. In this way the picture of interactions became localized, i.e., the cause of forces are fields at the point where the body is located at this moment in time.

Faraday has also observed that magnetic fields, changing with time can cause electric fields curling around the changing magnetic fields (Faraday's Law of induction), and Maxwell finally came up with a consistent model for the dynamics of the fields and the charge and current distributions causing them and how the fields mediate the electric and magnetic forces of charged and magnetized bodies.

At one point, when combining a lot of observations, he came to the conclusion that Ampere's Law, how to describe the magnetic fields as caused by electric currents (i.e., moving electric charge) had some important flaw, and that he had also to assume that a time-varying electric field must also cause magnetic fields, very similar to electric currents. Thus Maxwell interpreted a time-varying electric field as a "displacement current", causing magnetic fields in the very same way as electric currents (i.e., flowing electric charges). This is called the Ampere-Maxwell Law.

Also Faraday's Law of induction, of course, had been incorporated into Maxwell's beautiful equations. Now you can combine these findings! A time-changing magnetic field causes time-changing electric fields (Faraday's induction law), and these time-changing electric fields in turn cause magnetic fields! It turns out in this way that electric and magnetic fields make up one coupled set of quantities, nowadays called "the electromagnetic field", and that this field has its own existence as a dynamical entity in its own right as much as material bodies have their existence in everyday life.

In this way, his equations told Maxwell something completely unexpected! Namely that the electromagnetic fields propagate through empty space as a wave. Particularly these waves propagator away from the oscillating charges and currents causing them, and he even could calculate all properties of these "free" electromagnetic waves, namely that the electric and the magnetic field are always perpendicular to the direction of wave propagation, i.e., that the waves are "transversal". Also the velocity of propagation could be predicted, and to his total surprise, from seemingly unrelated measurements concerning electric and magnetic phenomena, leading to a parameter of the dimension of a speed in his model, it turned out that this speed is very close in value to the speed of light in the vacuum! More convincingly also all other properties of light turned out to be well-described by the assumption that light is nothing else than electromagnetic waves propagating in free space. In this way not only electricity and magnetism have been unified to classical electrodynamics (or better named electromagnetics) but also the whole field of wave optics, which before had been a totally independent topic in physics.

At the end of the 19th century on top the final confirmation of Maxwell's prediction of electromagnetic waves has been achieved by Heinrich Hertz, who could after a long struggle with his apparatus create free electromagnetic waves (with wavelengths at the meter scale) and prove the very properties, Maxwell had calculated as solutions to his equations (and he himself by also using Maxwell's theory).

I hope this lengthy "answer" to your question helps you to understand, how natural sciences are working, particulary how theory, observations, and experiments all work together to grasp some of the fundamental Natural Laws, and in which sense "why questions" can be answered by natural sciences. You never will get a final answer, why things are as they are but at least you know what really is (at least at some accuracy and with some limited validity of the so far observed and analyzed fundamental laws) and how observations can be understood from some very basic fundamental laws. These fundamental laws themselves cannot "explained" any further, at least not at the actual knowledge of science.

Maybe later there will be even better models and theories to understand these laws from even simpler and more comprehensive laws. In the case of electromagnetism that's in fact already the case nowadays. First of all in the beginning of the 20th century, by further analysis of Maxwell's equations, many physicists came to the conclusion that our understanding of the mathematics underlying the description of space and time by Newton had to be revised. This line of research has been finished by Einstein's Special Relativity Theory (SRT) in 1905.

Another puzzle in connection with electromagnetism has been solved by Planck in 1900 (after more than 30 years of research by a lot of physicists including himself!), namely how to understand the spectrum of electromagnetic waves emitted from hot bodies (like a piece of iron which starts to glow reddish at lower temperatures, which becomes blueish white at higher temperatures). As it turned out, even Maxwell's equations which are so successful in explaning almost all everyday phenomena concerning electromagnetic phenomena, are not accurate enough to understand this seemingly simple observation of the temperature dependence of the color of light emitted from a hot piece of metal! This observation, starting from Planck's solution of the heat-radiation problem, has caused the true revolution in physics of the 20th century and led to the discovery of quantum theory in the 1920ies (by Heisenberg, Schroedinger, Dirac, and many other physicists).

The best theory about electromagnetic phenomena, and for which no contradiction with observations has been found today, is the combination of Special Relativity and Quantum Theory in terms of what's called relativistic quantum-field theory, for the theory of charged particles and electromagnetic fields particularly Quantum Electrodynamics (QED). Some predictions of this theory, like the very accurate details of the electromagnetic radiation (spectral lines) emitted by hydrogen atoms, are accurate to 10 and more significant digits (like the frequency of certain electromagnetic transitions in hydrogen atom, a phenomenon known as the "Lamb shift")!

3. Jun 17, 2012

### cheah10

Wow! This reply really is informative! Although I don't know much of the histories you have told me up there, but I can see you really gave in a lot of effort on typing this one. Thanks a bunch! I appreciate it!