The electrostatic potential V at a point on t | vedclass

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(A) To find the total electrostatic energy,we consider building the disk by adding concentric rings of charge.Consider a disk of radius $r$ with unifo

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$U = \frac{8}{3}\pi \sigma^2 R^3$

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(A) To find the total electrostatic energy,we consider building the disk by adding concentric rings of charge.Consider a disk of radius $r$ with uniform surface charge density $\sigma$. The charge on a thin ring of radius $r$ and width $dr$ is given by:$dq = (2\pi r dr) \sigma$The potential at the circumference of a disk of radius $r$ is given as $V = 4\sigma r$. The work done to bring an additional charge $dq$ from infinity to the circumference of the disk is the electrostatic potential energy $dU$:$dU = V dq = (4\sigma r) \cdot (2\pi r dr \sigma) = 8\pi \sigma^2 r^2 dr$To find the total energy $U$ for a disk of radius $R$,we integrate from $r = 0$ to $r = R$:$U = \int_0^R 8\pi \sigma^2 r^2 dr = 8\pi \sigma^2 \left[ \frac{r^3}{3} \right]_0^R = \frac{8}{3}\pi \sigma^2 R^3$

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