- #1
yungman
- 5,751
- 290
I am referring to the book "Introduction to Electrodynamics" by Griffiths p317, Energy in magnetic field.
[tex]\Phi = \int_S \vec B \cdot d \vec a = \int_C \vec A \cdot d \vec l [/tex]
[tex] LI = \int_C \vec A \cdot d \vec l [/tex]
But the inductance in defined as the flux linkage divid by the current that create the flux or:
[tex] L = \frac {\Lambda}{I} [/tex]
If the inductor is N turn, [itex] \Lambda = N\Phi[/itex]
I want to verify according to the book that:
[tex] LI = \int_C \vec A \cdot d \vec l \Rightarrow W = \frac {1}{2} I \int_C \vec A \cdot d \vec l \Rightarrow W = \frac {1}{\mu_0}[\int_v B^2 d \tau - \int_S (\vec A X \vec B) \cdot d\vec a][/tex]
Only apply to a single loop inductor or a straight wire type that N=1. Because for multi turn N inductor, [itex] \Lambda = N\Phi[/itex]
[tex]\Phi = \int_S \vec B \cdot d \vec a = \int_C \vec A \cdot d \vec l [/tex]
[tex] LI = \int_C \vec A \cdot d \vec l [/tex]
But the inductance in defined as the flux linkage divid by the current that create the flux or:
[tex] L = \frac {\Lambda}{I} [/tex]
If the inductor is N turn, [itex] \Lambda = N\Phi[/itex]
I want to verify according to the book that:
[tex] LI = \int_C \vec A \cdot d \vec l \Rightarrow W = \frac {1}{2} I \int_C \vec A \cdot d \vec l \Rightarrow W = \frac {1}{\mu_0}[\int_v B^2 d \tau - \int_S (\vec A X \vec B) \cdot d\vec a][/tex]
Only apply to a single loop inductor or a straight wire type that N=1. Because for multi turn N inductor, [itex] \Lambda = N\Phi[/itex]