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Electric Flux And Gauss’ Law

Electric flux density at a point r meters from the point charge is

441.png 


Electric field intensity at a distance r from point charge in free space is

446.png 


Gauss’ Law

It states that, total flux out of a closed surface is equal to net charge within the surface.

451.png 

Divergence

.V = 456.png . (v1i + v2j + v3k)


Curl

Curl V = × V = 461.png
 

i.e. × V = 466.png × (v1i + v2 j v3k)
 

471.png
 

476.png

Gradient

 

If V is a scalar quantity, then gradient of v grad v = V
 

V = 481.png
 

where, 486.png called del operator.
 

Gauss’ Divergence Theorem

491.png 


Stoke’s Theorem

496.png 


Maxwell’s Equations in Differential (or point) Form and Integral Form

 

Poisson’s and Laplace’s Equations

.V = 537.png ...(1)


This equations (1) is called Poisson’s equation for a homogeneous equation.

542.png...(2)


This equation is called Laplace’s equation in rectangular coordinates and
2 is called Laplacian of V.





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