Gauss 's law     

                                       

what is Gauss law ? what are the application of Gauss law ?

A/c to the Gauss law electric flux passing through close surface is 1/εo times total charge enclosed by close surface . 
Electric flux through close surface is due to charge present inside closed surface. 
Electric field vector ( ε ) on L.H.s is due to all charge whether present inside or outside closed field. 
There are following application of Gauss law -:
1. To find symmetrical electric field . 
2. To apply Gauss law we choose close surface called Gaussian surface . 
3. Gaussian surface should be such that electric field has same value over Gaussian surface . 

 ☆ Gauss law derivation    

consider closed surface enclosing charge Q . for calculating electric flux passing through close surface . Draw sphere of radius r centred at charge Q . 
consider elementary surface of area ds . Electric field  (ε )vector and Area vector (ds vector) is directed radially outward .  

what are electric field lines ?

electric field lines are imaginary line which is pictorial mapping of electric field. 

what are the properties of electric field lines ? 

 There are following properties of electric field lines -: 

1. Tangent to the electric field lines is directed along the electric field at that point. 

2.Electric field intensity is directly proportional to no. of field lines passing through unit area perpendicular to the surface. 
 3. Electric field lines for single positive charge is radially outward and radially inward for single negative charge . 

                               

4.Electric field lines start from positive charge and end at negative charge .

5. Electric field line never forms closed loop due to conservative nature of electric field. 

6.Two electric field line can never intersect each other because at the point of intersection electric field has no unique direction . 

7. Electric field lines are continuous curve without any break because electric extend up to infinity . 

what is electric flux ?       

• electric flux is a property of a electric field which determine the number of field line passing through the surface .

• It is represented by symbol  Ø .

• It's s.i. unit is  (Vm ).

• formula of electric flux ( Ø ) = E.ds = Ecosθ.ds

• Number of electric field line passing through the surface ∝  Ecosθ.ds

• Dimensional formula of electric flux is given by [ ML3 T-3 L-1 ] .

How to find the electric flux passing through large surface ? 

 Here ,
Ecosθ = component of electric field perpendicular to the surface.
Esinθ = component of electric field in the plane of surface . 
consider the elementary surface of area ds which lies in electric field Ē ( E vector ) which makes angle of θ with perpendicular to the surface . 

for calculating electric flux passing through large surface , we divided large surface into large no. of elementary surface and electric flux passing through elementary surface is calculated .

Is electric flux a vector quantity ?  

Electric flux is a scalar quantity . It is a scalar because it is the dot product of the two vector quantity .

what is the use of electric flux ?

 It is use as a bypass paths for oscillating components of signals in circuitry. It is also used in photocopying machines and electrostatics precipitators . 

prove that a close surface does not enclose any charge , then electric flux passing through the close surface will be 0 

 consider sphere which lies in electric field does not enclose any charge 
1. divide sphere into two portion pqr and pmr 
2. No. of electric field line entering through portion pqr = no. of electric field line leaving the portion pmr .

I hope this will helpful for you .

Thank you for reading my post 

Any doubt regarding this post is always welcome .
 so  kindly ask your question (doubt) in the comment section.

suman kumar

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