Understanding the Larmor Formula: The Role of Field Line Connections

Click For Summary
SUMMARY

The discussion revolves around deriving the Larmor Formula, specifically addressing the connection of parallel field lines in the context of electromagnetic theory. The user references a diagram from Purcell's appendix B to illustrate their reasoning. The key point of contention is the assertion that equal flux in cones around the x-axis implies that field lines AB and CD are connected. The user seeks clarification on this reasoning, indicating a gap in understanding the relationship between flux and field line connectivity.

PREREQUISITES
  • Understanding of electromagnetic field theory
  • Familiarity with the Larmor Formula
  • Knowledge of flux concepts in physics
  • Ability to interpret diagrams related to field lines
NEXT STEPS
  • Study the derivation of the Larmor Formula in detail
  • Review electromagnetic field line theory and its implications
  • Examine the concept of magnetic flux and its mathematical representation
  • Analyze diagrams from Purcell's appendix B for better comprehension
USEFUL FOR

Students and educators in physics, particularly those focused on electromagnetism, as well as anyone seeking to deepen their understanding of field line connections and the Larmor Formula.

albega
Messages
74
Reaction score
0

Homework Statement


I need to derive this formula, and I'm basing it upon the following method (this has the diagram which I will be talking about below)
http://isites.harvard.edu/fs/docs/icb.topic1214926.files/Purcell-appendix-B.pdf

The Attempt at a Solution


I'm fine with everything apart from the reasoning that the parallel field lines (from where q is, and where it would be) have to join up in the middle region. The reasoning for this is given as

'A field line such as AB lies on a cone around the x-axis which includes a certain amount of flux from the charge q. If CD makes the same angle θ with the axis, the cone on which it lies includes the same amount of flux. Hence AB and CD must be parts of the same field line, connected by a segment BC.'

I don't see how the cones having equal flux implies the two field lines must be the same and so joined. Could anybody explain this? Thanks!
 
Physics news on Phys.org
Anyone please? It won't take too long to read the derivation!
 
I've tried a couple of times to view the PDF, but it comes up blank on my system. Maybe others have the same problem.
 

Similar threads

Question about Electric Field lines (MCQ)
  • · Replies 2 ·
Replies
2
Views
3K
Net charge contained by a cube in a region with a non-uniform E field
  • · Replies 3 ·
Replies
3
Views
3K
Uncharged capacitors connected in series
  • · Replies 18 ·
Replies
18
Views
3K
Calculating eletric potential using line integral of electric field
  • · Replies 1 ·
Replies
1
Views
2K
How to Apply Derivatives in Physics Problems?
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Magnetic field when the area of the plates of a capacitor increases
  • · Replies 7 ·
Replies
7
Views
2K
Gauss' Law --> Electric field of an infinitely long, straight line
  • · Replies 7 ·
Replies
7
Views
11K
Why field lines must begin or end on electric charges?
  • · Replies 1 ·
Replies
1
Views
4K
How Can Lambda be Derived from Gauss's Law for an Infinite Line of Charge?
  • · Replies 7 ·
Replies
7
Views
3K
Electric field above an off-center finite line charge
  • · Replies 5 ·
Replies
5
Views
3K