Electric Flux Entering Cone of Radius r and Height h

[jyothsna pb]

Homework Statement

what is the flux entering a cone of radius r and height h located in a uniform electric field E parallel to its base?

Homework Equations

flux = E.ds

The Attempt at a Solution

 

[ehild]

What is ds?

ehild

 

[gabbagabbahey]

Better yet, what does the divergence theorem tell you?

 

[jyothsna pb]

What is ds?

ehild

it is the small element of the effective area through which flux passes

 

[gabbagabbahey]

it is the small element of the effective area through which flux passes

He was hinting that your first step should be to find an expression for ds (if you evaluate the flux integral directly).

 

[ehild]

And what is the effective area of a curved surface like that of a cone?

ehild

 

[jyothsna pb]

dat is what i am confused of

 

[jyothsna pb]

i see 2 possibilities one the curved surface area of the cone and the other the triangular plane perpendicular to base but which one?

 

[ehild]

In your first formula dΦ= E˙ds is the product of E with the area normal to it. As the field lines are parallel to the base, these surface elements are parts of that triangular cross section of the cone which is perpendicular to the electric field. As E is constant simply multiply E with the area of the triangle.

 

[jyothsna pb]

thanx but one more doubt can't we take curved surface area resolved into the field direction in this case?

 

[ehild]

I do not quite follow you, but this is what we do. By definition, the flux is E ds cos (alpha) where alpha is the angle between E and the normal of the surface element. ds cos(alpha) is the projection of the surface area onto a plane normal to E.

ehild

 

[jyothsna pb]

thanku so much got the point now