Why Electric Flux \Phi is Defined

[yaik]

Why the electric flux $$\Phi$$ is defined as EAcos$$\theta$$?

I don't understand the part about cos$$\theta$$...

 

[ZapperZ]

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html#c3

It came from the dot product between E and dA, i.e. the projection of E along the differential area.

You may want to bookmark the entire Hyperphysics website.

Zz.

 

[tiny-tim]

Welcome to PF!

Hi yaik! Welcome to PF!

Imagine you want to know the flux of bugs flying horizontally along a road.

If you count the number that go splat on your windscreen, then you'll collect less (in a given time) if the windscreen is tilted: the number will be greatest at 90º, and zero at 0º: it'll be proportional to cosθ.

Mathematically, flux of a field E through a surface with area A is E.(Añ), where ñ is the unit vector normal (perpendicular) to the surface. ​

 

[yaik]

thx!

 

[sardar]

Electric flux \Phi is a concept used in the study of electromagnetism to describe the flow of electric fields through a given surface. It is defined as the product of the electric field strength and the area of the surface, multiplied by the cosine of the angle between the electric field and the surface normal. This definition is based on the fact that the electric field lines are perpendicular to the surface at any point, and therefore the component of the electric field that is parallel to the surface does not contribute to the flux. This is why the cosine of the angle is included in the equation.

The reason why electric flux is defined in this way is to accurately quantify the amount of electric field passing through a surface. By including the cosine of the angle, we are taking into account the orientation of the surface with respect to the electric field. If the surface is parallel to the electric field, the flux will be at its maximum value. If the surface is perpendicular to the electric field, the flux will be zero. This definition allows us to calculate the electric flux for any given surface and electric field configuration.

In addition, the inclusion of the cosine of the angle also allows us to account for the direction of the electric field. If the electric field is in the same direction as the surface normal, the flux will be positive. If the electric field is in the opposite direction, the flux will be negative. This is important in understanding the behavior and effects of electric fields on different surfaces and objects.

In summary, the definition of electric flux as EAcos\theta is necessary to accurately quantify the flow of electric fields through a surface and take into account the orientation and direction of the electric field. It is a fundamental concept in electromagnetism and is crucial in understanding and analyzing electric fields and their effects.