Induced Emf in a Loop of Circular Wire

[Gear300]

Induced Emf

For a loop of circular wire, there is a changing magnetic field running through it, but it is restricted to a region that is within the region of the loop of wire, so the field only runs through the loop of wire (it does not touch the loop of wire). Apparently, an emf is generated along the wire even though the magnetic field is not touching the wire. In the equations, the magnetic flux corresponds to the area of the of loop, so that would be the mathematical explanation, but how does that conceptually work? Would it be any different if the field were external to the wire instead?

 

[jbsteele]

The conceptually way it works is through Faraday's Law of Induction. This law states that a changing magnetic flux can induce an electromotive force (emf) in a conductor, which is the wire in this case. The magnetic flux is the number of magnetic field lines passing through an area, and if the magnetic field strength or direction changes, then the magnetic flux will change as well. When the magnetic flux changes, an emf will be generated along the wire. This emf will cause a current to flow in the wire, and this current will produce its own magnetic field which will oppose the changing external magnetic field. This is known as Lenz's Law. If the magnetic field were external to the wire instead, the same basic principle would apply. The changing magnetic field would still induce an emf in the wire, which would cause a current to flow in the wire. The current would then produce its own magnetic field, causing the external magnetic field to be opposed.

 

[Moetasim]

The phenomenon of induced emf in a loop of circular wire is known as Faraday's law of induction. This law states that a changing magnetic field will induce an emf (electromotive force) in a closed circuit. This means that when the magnetic field within the loop of wire changes, it creates a current in the wire, which can be measured as an emf.

Conceptually, this can be explained by understanding that a changing magnetic field creates a changing flux (magnetic field lines) through the loop of wire. This changing flux induces an electric field within the wire, which in turn creates an emf and a current. This is similar to how a generator works, where a rotating magnet creates a changing magnetic field, inducing an emf in the wire coils attached to it.

It does not matter if the magnetic field is external or within the loop of wire. As long as there is a changing magnetic field, an emf will be induced in the wire. However, the strength of the induced emf will depend on the strength and rate of change of the magnetic field.

In conclusion, induced emf in a loop of circular wire is a fundamental concept in electromagnetism and has many practical applications, such as in generators, transformers, and motors. It is a result of the relationship between changing magnetic fields and electric fields, as described by Faraday's law of induction.