Where Does the Self Inductance Formula Come From?

Click For Summary
SUMMARY

The self-inductance formula for a solenoid is derived from the relationship between magnetic flux and current. The magnetic field inside the solenoid is given by B = μ₀ NI/l, where μ₀ is the permeability of free space, N is the number of turns, I is the current, and l is the length of the solenoid. The magnetic flux through one loop is calculated as Φ = BA = μ₀ NIA/l, leading to the total flux of Φ = μ₀ N²IA/l. The inductance L is defined as the total flux divided by the current, resulting in the formula L = μ₀ N²A/l.

PREREQUISITES
  • Understanding of electromagnetic theory
  • Familiarity with solenoid geometry
  • Knowledge of magnetic flux concepts
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the derivation of the Biot-Savart Law
  • Learn about the applications of inductance in electrical circuits
  • Explore the concept of mutual inductance
  • Investigate the effects of core materials on inductance
USEFUL FOR

Physics students, electrical engineers, and anyone interested in understanding electromagnetic induction and solenoid behavior.

nabliat
Messages
30
Reaction score
0
Physics news on Phys.org
[itex]A[/itex] is the cross sectional area of the solenoid/telephone cord, and the magnetic field inside the solenoid is [itex]B=\mu_0 NI/l[/itex] so the flux through one loop in the solenoid is [itex]BA=\mu_0 N IA/l[/itex] so the total flux is [itex]\Phi= \mu_0 N^2 I A/l[/itex] and the inductance is just total flux divided by current.
 
thanks
 

Similar threads

Undergrad Guidance Requested on Inductance Formula for Solenoid
  • · Replies 2 ·
Replies
2
Views
2K
Engineering Inductance of a layered Solenoid?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Mutual inductance in a transformer
  • · Replies 16 ·
Replies
16
Views
5K
Self excited induction generators and grid connected solar inverters?
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad Question about Capacitor current and electromagnetic induction
  • · Replies 16 ·
Replies
16
Views
2K
Extracting capacitance and inductance from s-parameters
  • · Replies 4 ·
Replies
4
Views
656
Comparing self inductance of three solenoids
  • · Replies 34 ·
2
Replies
34
Views
4K
Use relativity and the Larmor formula to calculate Lienard's formula
  • · Replies 2 ·
Replies
2
Views
2K
EM: Separation of variables to find magnetic induction
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Need a good idea : 3D simulation of Inductive wireless power transfer
  • · Replies 6 ·
Replies
6
Views
2K