I recently found that surface area of a sphere can't be found with the following method. What's the flaw in it? First, I have taken a very thin ring of thickness $dx$ at a distance of $x$ from the centre. Then, I integrated it, using substitution of $x=R\sin\theta$
But this is giving me answer $4\pi^2R^2$.
I also tried to solve many other problems related to area of sphere, like I found the magnetic field at the centre due to a revolving sphere carrying a charge $Q$, but this method is giving me wrong result.
The correct result is found by taking a thin ring subtending an angle $2\theta$ at centre, and thickness of the ring would be $Rd\theta$.
But, why my method is not giving the correct answer?
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