Electrodynamics flux calculation question

[AHSAN MUJTABA]

Homework Statement

Consider a right circular cone placed such that the symmetry axis is
the z axis. The base of the cone is centered at the origin with a radius of R. The
pointed end of the cone is at the location z = h. A point charge q is placed at the point
(0, 0, h/3). Show that the integral form of the Gauss's law holds by computing the
flux over the conical surface.

Relevant Equations

integral(E.n da )=Q/e I need toprove it

I don't really know how to find it mathematically as I am really confused in finding the normal vector and finding the electric field as well.
pls help

 

[berkeman]

Homework Statement:: Consider a right circular cone placed such that the symmetry axis is
the z axis. The base of the cone is centered at the origin with a radius of R. The
pointed end of the cone is at the location z = h. A point charge q is placed at the point
(0, 0, h/3). Show that the integral form of the Gauss's law holds by computing the
flux over the conical surface.
Relevant Equations:: integral(E.n da )=Q/e I need toprove it

I don't really know how to find it mathematically as I am really confused in finding the normal vector and finding the electric field as well.
pls help

Welcome to PhysicsForums.

It seems like a pretty straightforward surface integration, no? What coordinate system do you think you can choose to make the integral a little easier?

Also, when typing equations into the PF Edit window, it's best to use the Latex Guide that is linked at the bottom of the window to help you type your math equations in a much more readable form. For example, Gauss' Law:

https://en.wikipedia.org/wiki/Gauss's_law

 

[AHSAN MUJTABA]

I am actually pretty confused because If I take cylinderical coordinates then what would be limits of R and I am also confused by the position of charge at h/3

 

[berkeman]

Can you show the calculation if the surface were just a sphere centered at the origin and the charge was at the origin? (use spherical coordinates)

And then can you show the calculation if the surface were a cylinder centered at the origin, and the charge was at the origin? (use cylindrical coordinates)

 

[haruspex]

I am actually pretty confused because If I take cylinderical coordinates then what would be limits of R and I am also confused by the position of charge at h/3

Your first step, as ever, is a diagram. In this case, just a vertical slice through the middle, to produce a triangle. Draw a field line from the charge to the cone. Relate the angle of incidence to the angle, θ, the field line makes to the z axis.
Draw a second line at θ+dθ.
Consider the surface element these delimit rotated around the z axis to produce a band. What is the net field through it?

 

[AHSAN MUJTABA]

do we have to take the cos component of electric field. I am still confused regarding the geometry.

 

[haruspex]

do we have to take the cos component of electric field. I am still confused regarding the geometry.

Did you draw the diagram I described? Remember, it is a right circular cone.
Please post your diagram, labelling the origin, the point charge, the tip of the cone, the points where the two field lines meet the surface of the cone, and some angles.