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MIT Physics 8.02 - Electricity & Magnetism

SECTION : Faraday's Law     

SUBJECT: Creating a Magnetic Field  

Suppose we have five rings that carry a number of free positive charges that are not moving. Since there is no current, there is no magnetic field. Now suppose a set of external agents come along (one for each charge) and simultaneously spin up the charges counterclockwise as seen from above, at the same time and at the same rate, in a manner that has been pre-arranged. Once the charges on the rings start to accelerate, there is a magnetic field in the space between the rings, mostly parallel to their common axis, which is stronger inside the rings than outside. This is the solenoid configuration.

As the magnetic flux through the rings grows, Faraday's Law tells us that there is an electric field induced by the time-changing magnetic field that is circulating clockwise as seen from above. The force on the charges due to this electric field is thus opposite the direction the external agents are trying to spin the rings up in (counterclockwise), and thus the agents have to do additional work to spin up the rings because they are charged. This is the source of the energy that is appearing in the magnetic field between the rings-the work done by the agents against the "back emf".

Over the time when the magnetic field is increasing in the animation, the agents moving the charges to a higher speed against the induced electric field are continually doing work. The electromagnetic energy that they are creating at the place where they are doing work (the path along which the charges move) flows both inward and outward. The direction of the flow of this energy is shown by the animated texture patterns. This is the electromagnetic energy flow that increases the strength of the magnetic field in the space between the rings as each positive charge is accelerated to a higher and higher velocity.



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