Understanding Faraday's Law: Implications for Motional EMF Explained

Click For Summary
SUMMARY

Faraday's Law of Electromagnetic Induction states that the electromotive force (EMF) generated in a closed loop is equal to the negative rate of change of magnetic flux through the loop. The integral form of Faraday's Law is expressed as ∫E·dl = -(d/dt)∫B·dA, which remains valid even when the area is changing, as long as the line integral corresponds to the perimeter of the area being integrated. This principle is crucial for understanding motional EMF, where a conductor moves through a magnetic field, generating EMF. Stokes' Theorem is applicable in deriving the differential form of Faraday's Law.

PREREQUISITES
  • Understanding of Faraday's Law of Electromagnetic Induction
  • Familiarity with Stokes' Theorem
  • Basic knowledge of electromotive force (EMF)
  • Concept of magnetic flux and its calculation
NEXT STEPS
  • Study the applications of Faraday's Law in electrical engineering
  • Learn about the implications of Stokes' Theorem in electromagnetism
  • Explore the concept of motional EMF in practical scenarios
  • Investigate the relationship between magnetic fields and induced currents
USEFUL FOR

Students of physics, electrical engineers, and anyone interested in the principles of electromagnetism and their applications in technology.

SpartanG345
Messages
69
Reaction score
1
My textbook said Faradays law EMF = integral of E.dl is only valid if the integration path is stationary.

Could someone explain what this means? Does it mean if the conductor changes shape Faraday law is not valid?

In motional EMF a conductor moves through a magnetic field and a EMF is generated, this can also be explained using Faraday's law
 
Physics news on Phys.org
Faraday's Law in integral form is written

∫E·dl = -(d/dt)∫B·dA

where the line integral on the left side is exactly around the perimeter of the area being integrated on the right side. This can be seen by applying Stokes' Theorem (see Eq 7 in)

http://mathworld.wolfram.com/StokesTheorem.html

from which the differential form of Faradays Law is easily derived. So as long as the line represented on the left side is the perimeter of the area on the right side, even if the area is changing (moving), the integral form of Faraday's Law is valid.

Bob S
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
667
  • · Replies 6 ·
Replies
6
Views
1K
  • · Replies 27 ·
Replies
27
Views
3K
  • · Replies 25 ·
Replies
25
Views
2K
  • · Replies 6 ·
Replies
6
Views
6K
  • · Replies 2 ·
Replies
2
Views
7K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 9 ·
Replies
9
Views
4K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K