Question

Figure shows a annular disc of outer radius $R$ inner radius $r$ , and uniform surface charge density. Total charge is $q$ . The potential at the centre is $\frac{k q}{r '}\left(k = \frac{1}{4 \pi \left(\epsilon \right)_{0}}\right)$ where $r'$ is

• A. $\frac{R + r}{2}$
• B. $\frac{R - r}{2}$
• C. $R+r$
• D. $R-r$

Answer 1

Answer: (A)

$V=k\displaystyle \int _{x = r}^{R}\frac{\sigma \cdot 2 \pi x d x}{x}=k\cdot \sigma 2\pi \left(\right.R-r\left.\right)$