Propagation Nature Of Electric Field And Magnetic Field

This post is about irrotational and solenoidal behavior of Electric field and Magnetic field respectively which is also explain Maxwell’s second and fourth equation.

Closed line integral (MAXWELL’S SECOND EQUATION)

$\oint \vec{E} \cdot \vec{dl}=0$

Potential difference can exit between two different and distinct points but with the same point, it is always zero. Potential is UNIQUE at a time. Work done in moving a charge in any closed line is always zero. The difference integration has equal positive and negative values such that ENERGY ACQUIRED in the field direction is equal to the ENERGY LOST opposite to field.

Energy acquired in field direction = Energy lost to field opposite

Electric field is CONSERVATIVE and IRROTATIONAL in nature

$\oint \vec{E} \cdot \vec{dl}= \iint(\nabla\times E)\cdot{d s} =0$

$\nabla\times\vec{E}=0$

The directional derivative of vector E never exist perpendicular to E.

$\oint\vec{E}\cdot{d l}=0$

This is KVL equivalent in Field Theory.

CLOSED SURFACE INTEGRAL FOR Magnetic Flux B AND MAXWELL THIRD EQUATION:

Magnetic field lines are always closed lines and are never ending . No chance of storing some where NO SHRINKING AT ALL.

$\int{B}\cdot{d l}=\psi_m$

Magnetic field lines are closed in nature such that in closed surface

                                 Entering flux = Leaving flux


$\oint_{surface}\vec{B}\cdot\vec{d s}=\int_{volume}(\nabla\cdot{B}){d v}=0$

The magnetic lines are never divergent or convergent i.e. no source/no shrink they are always in circular shape that means magnetic lines are solenoidal in nature.

$\nabla\cdot{B}=0$

The directional derivative of B does not exist in direction of B.

NOTE : Equivalents of single charges or magnetic monopoles do not exist. Every cause of B field is “DIPOLE NATURED”. Current is cause of magnetic fields and flows only in closed loops when both the polarities exist. For flow of electric current , a battery having positive as well negative polarity has to exist. If only one polarity is existing, current can not flow and magnetic field don’t exist.

$\oint{B}\cdot{d s}=0$ is KCL equivalent in Filed theory.

Categories: Electromagnetism