Surface area problem -- Area of the circle enclosed by the current produced by an electron in a hydrogen atom

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Anthill
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What does the shape that has, in polar coordinates, a given surface area look like?
My textbook says "A is the area of the circle enclosed by the current" (produced by an electron in a hydrogen atom), A = ##\pi r^2 \sin(\theta)^2##. I don't understand where the ##\sin(\theta)^2## comes from.
 

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  • #2
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Summary:: What does the shape that has, in polar coordinates, a given surface area look like?

My textbook says "A is the area of the circle enclosed by the current" (produced by an electron in a hydrogen atom), A = ##\pi r^2 \sin(\theta)^2##. I don't understand where the ##\sin(\theta)^2## comes from.
Assuming that the radius of the circle is x, the area would be ##A = \pi x^2##.

Converting to polar coordinates, ##x = r \sin(\theta)##, so ##x^2 = r^2 \sin^2(\theta)##, and the area would be ##\pi r^2\sin^2(\theta)##.
Note that powers of trig functions are usually denoted like this: ##\sin^2(\theta)## rather than this ##\sin(\theta)^2##.
 

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