University:
Santa Fe College
Course:
ETS 2527C | Electromechanical Components and Mechanisms
Academic year:

2024
Views:

492

Pages:

7
Author:

Jabin F.

# Magnetic vector potential (A) Scalar potential (v) for a possible magnetic field 0 ord=0 B.de = magnetic flux S = no. of magnetic field Uner associated with the surface. N \[\oint_{s}\vec{B}\cdot d\vec{s}=0\] \[\Rightarrow\int(\vec{\nabla}\cdot\vec{B})d\tau=0\] \[\Rightarrow\vec{\nabla}\cdot\vec{B}=0\] Non-existence of magnetic monopoles. example: H-atom If we put in closeal surface then \[\oint_{s}\vec{B}\cdot d\vec{s}=0\] (non-existence of magnetic monopole) Since \(\vec{\nabla}\cdot\vec{B}=0\) can be written as \[\vec{\nabla}\times(\vec{\nabla}\times\vec{A})=0\] Magnetostatic \[\oint_{s}\vec{B}\cdot d\vec{l}=0\Rightarrow\vec{\nabla}\times\vec{B}=\mu_{0}\vec{J}\] \[\oint_{s}\vec{B}\cdot d\vec{l}=\mu_{0}I\] in Electro static \[\vec{\nabla}\cdot\vec{E}=\frac{\rho}{\epsilon_{0}}\], \(\vec{\nabla}\times\vec{E}=0\) \[\vec{E}=-\vec{\nabla}v\] \[\vec{\nabla}\times(-\vec{\nabla}v)=0\] curl of grodian \[\vec{\nabla}\cdot\vec{B}=0\Rightarrow\vec{B}=\vec{\nabla}\times\vec{A}\] diff. form \[\Rightarrow\vec{\nabla}\cdot(\vec{\nabla}\times\vec{A})=0\] \[\int_{s}\vec{B}\cdot d\vec{l}=\int_{s}(\vec{\nabla}\times\vec{A})\cdot d\vec{s}\] \[\Rightarrow\oint_{c}\vec{B}\cdot d\vec{l}=\int_{s}\vec{A}\cdot d\vec{s}\] integral form Magnetic flux (\(\Phi_{m}\))=\int_{s}\vec{B}\cdot d\vec{s}=\int_{s}(\vec{\nabla}\times\vec{A})\cdot d\vec{s}\] \[\vec{\nabla}\cdot\vec{A}=0\Rightarrow\frac{d}{dt}\int_{s}\vec{A}\cdot d\vec{s}=0\] Scalar potential \(V=\frac{W}{q}\] Vector potential \(\vec{A}=\frac{\vec{p}}{q}\]