Electromagnetics coulombs law and field intensity

[Alwaysprolol]

Homework Statement

The circular region, ρ < a, z= 0, carries a uniform surface charge density ρ ( subscript s). Find E at P(0,0,h), h > 0.

Homework Equations

Coulombs law
Field of a line charge and field of a sheet charge.

The Attempt at a Solution

I'm not sure what they are asking for , but my attempt I used the equation for a field of a sheet of charge cause it's the only one provided in the Homework that contains the ρ (subscript s).

It says E at point (0,0,h) so I'm guessing since its at z = 0 then the vector would be (0,0,h-0). Resulting in my result of

E = (ρ(subscript s) / 2ε ) (0,0,h)

Im not really sure what I'm supposed to be finding

 

[Alwaysprolol]

Okay so I get a little bit, I'm looking for the E of a circular region with the radius of ρ ?

 

[SammyS]

Homework Statement

The circular region, ρ < a, z= 0, carries a uniform surface charge density ρ ( subscript s). Find E at P(0,0,h), h > 0.

Homework Equations

Coulombs law
Field of a line charge and field of a sheet charge.

The Attempt at a Solution

I'm not sure what they are asking for , but my attempt I used the equation for a field of a sheet of charge cause it's the only one provided in the Homework that contains the ρ (subscript s).

It says E at point (0,0,h) so I'm guessing since its at z = 0 then the vector would be (0,0,h-0). Resulting in my result of

E = (ρ(subscript s) / 2ε ) (0,0,h)

I'm not really sure what I'm supposed to be finding

Hello Alwaysprolol. Welcome to PF !

(Use the X² and X₂ icons for superscripts & subscripts.)

Using the E field for an infinite sheet gives the wrong answer.

Do you have an expression for the E field along the axis of a ring of charge?

 

[Alwaysprolol]

Hello Alwaysprolol. Welcome to PF !

(Use the X² and X₂ icons for superscripts & subscripts.)

Using the E field for an infinite sheet gives the wrong answer.

Do you have an expression for the E field along the axis of a ring of charge?

Thanks!

Unfortunately, I was not given one. The professor has given us only equations for E of a line charge and a sheet and I'm not quite sure how to utilize them in this question since its asking for the E in a circular region

 

[Nickie]

either. I would need more context and information to provide a comprehensive response. However, based on the given information, it seems like you are trying to find the electric field at point P(0,0,h) in a circular region with a radius of a and a uniform surface charge density of ρ. In this case, you would use Coulomb's law to calculate the electric field at point P, which would be given by E = kq/r^2, where k is the Coulomb's constant, q is the charge, and r is the distance between the point and the source of the electric field. In this case, the source of the electric field would be the circular region with a surface charge density of ρ. You would need to integrate over the circular region to find the total charge and then use that value in Coulomb's law to calculate the electric field at point P. Alternatively, you could also use Gauss's law to find the electric field at point P, which would be given by E = ρ/ε, where ρ is the charge density and ε is the permittivity of the medium. Again, you would need to integrate over the circular region to find the total charge density and then use that value in Gauss's law to calculate the electric field at point P.