Find expression for electric field given B(t)

Click For Summary
SUMMARY

The discussion centers on deriving the electric field expression given a magnetic field B(t) using Stokes' theorem. The relevant equation is identified as the integral of E dot dl equating to the integral of -dB/dt dot dA. A critical error noted is the incorrect representation of B in the equation, which should be -dB/dt, and the direction of the line element dl, which must adhere to the counterclockwise convention with the positive z-axis out of the paper. These adjustments are essential for accurate application of the theorem.

PREREQUISITES
  • Understanding of Stokes' theorem in electromagnetism
  • Familiarity with line integrals and surface integrals
  • Knowledge of the relationship between electric fields and changing magnetic fields
  • Basic concepts of vector calculus
NEXT STEPS
  • Study the application of Stokes' theorem in electromagnetic contexts
  • Learn about the implications of Faraday's law of induction
  • Explore the mathematical derivation of Maxwell's equations
  • Investigate the physical significance of line and surface integrals in electromagnetism
USEFUL FOR

Students of electromagnetism, physics educators, and anyone involved in advanced physics problem-solving, particularly in the context of electric and magnetic field interactions.

mkematt96
Messages
25
Reaction score
0
Capture.JPG

Homework Statement


See picture above

Homework Equations


Int (E dot dl) = Int (B dot dA)

The Attempt at a Solution



Where did I go wrong? Is there a sign error possibly or am I off conceptually? [/B]
File_000.jpeg
 
Physics news on Phys.org
The only thing I see that is incorrect is in your relevant equations (2), it should say ## -dB/dt ## instead of ## B ##. Their ## dl ## in the figure is in the opposite direction of what it should be, but I don't think that is your mistake. The line integrals in these Stoke's formulas always go counterclockwise with +z out of the paper. Perhaps the instructor wanted you to spot that anomaly, etc...
 

Similar threads

  • · Replies 14 ·
Replies
14
Views
3K
Replies
12
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 11 ·
Replies
11
Views
4K
  • · Replies 6 ·
Replies
6
Views
3K
Replies
6
Views
2K
  • · Replies 5 ·
Replies
5
Views
4K
  • · Replies 5 ·
Replies
5
Views
1K
Replies
5
Views
4K