Electric flux in physics with problems and solutions

What is Electric Flux?

“Total number of field lines passing through a certain element of area is called flux”.

It may also be defined as “The scalar product of electric field intensity E and vector area  A“.

Electric flux dimensional  formula

It is denoted by Greek letter Φ.

Φ=E.A

Φ=EAcosθ

Where θ is the angle between E and A.Electric flux is a scalar quantity.

What is the unit of electric flux?

Its SI unit Nm²/c.Below figure showing electric flux through a surface normal to E.

 

When we place an element of an area in an electric field ,some of the lines of force pass through it.In order to give a quantitative meaning to flux ,the field lines are drawn such that  the number of field lines passing through a unit area held perpendicular to field lines at a point represent the intensity E of  the field at that point.Suppose at a given point the value of E is 4N/C .This means that if 1m² area is held perpendicular to the field lines at this point,4 field lines will pass through it.

 

Maximum Flux

Consider a certain area A is held perpendicular to the field lines E but direction of A is parallel to E  as shown in figure below.

In this case ,angle between E and  A is O°

Φ=EAcosθ

Φ=EAcos0°

Φ=EA.1

Φ=EA

Minimum Flux

If area is held parallel to the field lines E ,shown in figure below

 

In this case  angle between E and A is 90°.

Thus                                                             Φ=EAcosθ

Φ=EAcos90°

We know cos90°=0

Φ=0

Now we consider the case in which A is neither perpendicular nor parallel to field lines but is inclined at angle θ with the lines as shown in figure

 

In this case we have to find the projection of the area A which is perpendicular to the field lines.The area of this projection  is

Acosθ.The flux Φ in this case is

Φ=EAcosθ=EA

Where θ is the angle between the field lines and normal to the area.

Electric flux formula with applications (video)