Question about induced current

[Feldoh]

Say we have an induced circuit. My book states that we cannot use the loop rule on an induced circuit because we cannot define a potential difference in the circuit. If the potential difference is undefined how can current exist?

There's probably a really obvious answer, but I'm not seeing it.

 

[cabraham]

Say we have an induced circuit. My book states that we cannot use the loop rule on an induced circuit because we cannot define a potential difference in the circuit. If the potential difference is undefined how can current exist?

There's probably a really obvious answer, but I'm not seeing it.

The potential is defined as long as a path is specified. In electric fields due to charged particles with no time-changing magnetic fields present, the potential from a to b is well defined as it is independent of the path of integration. This electric field is called conservative, and it has no "curl, aka rotation or circulation".

When ac magnetic fields are present there must also be an electric field present. This E field is non-consevative, and has "curl", or rotation, circulation if you prefer. The potential is the line integral around the loop, and is path dependent. A path which encloses a larger area encloses a larger magnetic flux, in webers, and the potential is larger.

If a closed loop having resistance R is subjected to an ac magnetic field, current will be induced. The potential around the loop is defined as long as a specific path is considered. Ohm's law is always upheld so that the voltage around the loop divided by the current always equals R. The potential is the work done per unit charge transporting the charge around the loop *along a specific path*. Again if no ac magnetic fields were present the potential around a closed loop equals zero independent of path taken. Kirchoff's voltage law is a special case of Faraday's law.

If this gives you trouble at first, don't feel bad. Great minds struggle with induction. I know degreed EE's practicing for decades who still have only a partial understanding of induction. Have I answered your question? BR.

Claude

 

[astrokreng]

The concept of induced current is based on Faraday's law of electromagnetic induction, which states that a changing magnetic field can induce an electric current in a conductor. In an induced circuit, the potential difference is not defined in the traditional sense, as it is not due to a battery or other external source. Instead, it is created by the changing magnetic field.

While we cannot apply the loop rule as we do in traditional circuits, we can still use other laws and principles, such as Kirchhoff's laws, to analyze the behavior of induced circuits. The key is to understand that the potential difference in an induced circuit is not due to a defined voltage source, but rather the changing magnetic field.

Furthermore, the existence of current in an induced circuit does not depend on the potential difference being defined. As long as there is a changing magnetic field, there will be an induced current. This is because the moving magnetic field creates a force on the free electrons in the conductor, causing them to flow and create a current.

In summary, while we cannot use the loop rule in an induced circuit, there are other principles that allow us to analyze and understand the behavior of induced currents. The potential difference may not be defined in the traditional sense, but it is still a crucial factor in the generation of induced currents.