Lorrain & Corson: Help with Derivation of Fig 18.9/7.20

  • Context: Graduate 
  • Thread starter Thread starter classy cal
  • Start date Start date
Click For Summary
SUMMARY

The discussion focuses on the derivation of Figure 18.9 (Figure 7.20 in the second edition) from Lorrain & Corson, specifically addressing the substitution of the element dl with acos(phi)dphi in Equations 18.36 and 18.37 (7.99 and 7.100). The key insight is that dl represents a magnitude of a dφ, and the derivation emphasizes the importance of the y-component of A, which incorporates the factor of cos(φ). Additionally, the text clarifies that the x-component of A is zero, as explained between equations 7.99 and 7.100.

PREREQUISITES
  • Understanding of vector calculus, particularly in relation to physics.
  • Familiarity with Lorrain & Corson’s "Electromagnetic Fields" textbook.
  • Knowledge of trigonometric functions, specifically cosine and their applications in physics.
  • Basic comprehension of components of vectors in two-dimensional space.
NEXT STEPS
  • Review the derivation of vector components in electromagnetic theory.
  • Study the relationship between angles and their corresponding trigonometric functions in physics.
  • Examine the context and applications of Equations 18.36 and 18.37 in electromagnetic fields.
  • Explore additional resources on vector calculus to reinforce understanding of the concepts discussed.
USEFUL FOR

Students and educators in physics, particularly those studying electromagnetism, as well as anyone seeking clarity on vector calculus applications in physical contexts.

classy cal
Messages
7
Reaction score
0
can someone help me with a derivation in L&C. I am wrestling with Figure 18.9 (Fig 7.20 in second edition) . In Equations 18.36 and 18.37 (7.99 and 7.100), the element dl is substituted with acos(phi)dphi and I cannot see how this is derived.
 
Physics news on Phys.org
Welcome to Physics Forums! I have the 2nd edition of this book.

dl has a magnitude of a dφ. Moreover, we are only interested in the y-component of A, hence the additional factor of cos(φ). (The book explains, between equations 7.99 and 7.100, why the x-component of A must be zero.)
 
Many thanks Redbelly.
 

Similar threads

How Is the Schrödinger Equation Derived from the Hamilton-Jacobi Equation?
  • · Replies 3 ·
Replies
3
Views
2K
Mathematica This Week's Finds in Mathematical Physics (Week 236)
  • · Replies 7 ·
Replies
7
Views
4K
Mathematica This Week's Finds in Mathematical Physics (Week 236)
  • · Replies 9 ·
Replies
9
Views
4K