- #1
IniquiTrance
- 190
- 0
I know that [tex] \int_{S}^{}\int_{}^{}\vec{B}\cdot d\vec{A} = 0 [/tex] because [tex] \textbf {div} \vec{B}=0 [/tex]
IE, because [tex] \Phi_{B} [/tex] leaving a closed surface must equal [tex]\Phi_{B}[/tex] entering.
Yet how is it then that [tex]\int_{C}^{}\vec{B}\cdot d\vec{l}[/tex] isn't also equal to zero?
Shouldn't it be true for any closed path that the amount of magnetic field lines leaving the perimeter of the path be equal to the amount entering, so that there be no net amount of field lines across it?
If it is true for a closed surface, shouldn't it be true for a closed path?
Thanks!
IE, because [tex] \Phi_{B} [/tex] leaving a closed surface must equal [tex]\Phi_{B}[/tex] entering.
Yet how is it then that [tex]\int_{C}^{}\vec{B}\cdot d\vec{l}[/tex] isn't also equal to zero?
Shouldn't it be true for any closed path that the amount of magnetic field lines leaving the perimeter of the path be equal to the amount entering, so that there be no net amount of field lines across it?
If it is true for a closed surface, shouldn't it be true for a closed path?
Thanks!