- #1
Saitama
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Homework Statement
I have to find the electric field at the center of a hemisphere of radius R with charge density σ.
Homework Equations
The Attempt at a Solution
The easiest way would be to select a ring element of small thickness, find the electric field due to it and integrate.
I am trying to do it by an another method. Let's select a small element of area dA subtending a solid angle dΩ at the center, then
[tex]dA=(dΩ)R^2[/tex]
Charge of this small element is σdA=σ(dΩ)R^2.
Therefore, electric field due to this element is
[tex]dE=\frac{kσ(dΩ)R^2}{R^2}[/tex]
The last job is to resolve the electric field into two components (see attachement) and integrate them separately but i am stuck here. I can't proceed after this because of the cosθ and sinθ.