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Electric flux in physics with problems and solutions

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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 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.ELECTRIC FLUX

 

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 areais held perpendicular to the field lines E but direction of A is parallel to E  as shown in figure below.MAXIMUM ELECTRIC FLUX

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 belowMINIMUM FLUS

 

In this case  angle between 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 figureRLRCTRIC FLUX THROUGH AN INCLINED SURFACE

 

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)

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