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Homework Statement
Given a solid hemisphere with radius R and uniform charge density ##/rho##, find the electric field at the center.
Homework Equations
##E = \frac{1}{4 \pi \epsilon_{0}} \frac{Q}{r^{2}}##
##E = \frac{1}{4 \pi \epsilon_{0}} \int \frac{\rho (x',y',z') \hat{r} dx' dy' dz'}{r^{2}}##
The Attempt at a Solution
The strategy is to slice the hemisphere into rings around the symmetry axis, then find the electric field due to each ring, and then integrate over the rings to obtain the field due to the entire hemisphere.
I am confused by the diagram, though:
It says that a rectangle with side lengths dr and r dθ is the cross-sectional area, and that this cross-sectional area multiplied by 2πrsinθ is the volume, since the radius of the ring is rsinθ. However, isn't this just the circumference multiplied by the cross-sectional area? There is no thickness of the ring, so is it a volume? Are there more rings within the ring, towards the axis? (Like smaller rings within larger rings.) How come the thickness isn't mentioned here?