How to Maximize Inductance in a Coaxial Cable?

Click For Summary
SUMMARY

The discussion focuses on maximizing the inductance (L) per unit length of a coaxial cable with an inner cylinder radius of 'a' and an outer cylinder radius of '4a', filled with a relative permeable material (μ(r) > 1) in the region of radius '2a < r < 3a'. To solve the problem, participants are encouraged to derive the inductance equation for a coaxial cable, express L as a function of radial geometry (L = L(r)), and differentiate it to find conditions for maximizing L. The discussion emphasizes the importance of understanding the geometric constraints and the distribution of magnetic material to achieve the largest inductance.

PREREQUISITES
  • Understanding of coaxial cable geometry and inductance calculations
  • Familiarity with magnetic permeability concepts
  • Knowledge of differentiation and optimization techniques in calculus
  • Ability to apply electromagnetic theory to practical problems
NEXT STEPS
  • Study the derivation of the inductance formula for coaxial cables
  • Learn about the effects of magnetic permeability on inductance
  • Explore optimization techniques in calculus for maximizing functions
  • Review practical applications of inductance in electrical circuits
USEFUL FOR

Students studying electromagnetism, electrical engineers, and anyone involved in designing or analyzing coaxial cable systems and inductors.

JH2o
Messages
1
Reaction score
0
hiya guys,

I'm having a large amount of trouble with a problem that I've been working through (currently revising for an uncoming exam in electromagnetism, along with a lot of other things). the problem is stated as follows (condensed):

coaxial cable - inner cylinder radius a, out cylinder radius 4a
region of radius 2a < r < 3a filled with relative permeable material mu(r) > 1

find the inducance L per unit length when cable is in a circuit with current in axial symmetry out along one cylinder and returning along the other.

suppose there is only enough magnetic material availble to this inductor, explain why L can be increased by distribution and find the largest inductance acheivable by doing so.

any light towards where to even start on this would be great!

thanks
 
Physics news on Phys.org
This homework problem is dated - Mar 29, 2007.

PF requires students to write the appropriate/relevant equations and for one to demonstrate effort.

Here it would help for one to write the equation for inductance in a coaxial cable. If one can express the equation for L as a function of the radial geometry, i.e., L = L(r), subject to the geometric constraints/limits, e.g., 0 < r < a, 2a to 3a, up to 4a, then should be able to differentiate with respect to the independent variable and find the conditions to maximize L.

See an example for writing such an equation -
https://eng.libretexts.org/Bookshel...atics/7.14:_Inductance_of_a_Coaxial_Structure
 
Reply
  • Like
Likes   Reactions: berkeman

Similar threads

Surface Charges on a Coaxial Cable
  • · Replies 1 ·
Replies
1
Views
3K
Magnetic energy density, self-inductance of coaxial cylindrical shells
  • · Replies 10 ·
Replies
10
Views
2K
Electric field of a coaxial cable
  • · Replies 1 ·
Replies
1
Views
3K
Coaxial cable conductors with dielectric: polarization of charge
  • · Replies 10 ·
Replies
10
Views
2K
Power Transmitted in a Coaxial Cable
  • · Replies 7 ·
Replies
7
Views
4K
Power transported down a coaxial cable
  • · Replies 8 ·
Replies
8
Views
3K
Calculating Self-Inductance in Coaxial Cables
  • · Replies 3 ·
Replies
3
Views
3K
Self inductance of a coaxial system of cylinders
  • · Replies 10 ·
Replies
10
Views
4K
Capacitance of Coaxial Cable Configuration with Multiple Conductors
  • · Replies 1 ·
Replies
1
Views
4K
Inductance of Solenoid on Coaxial Cable
  • · Replies 9 ·
Replies
9
Views
6K