Question

In a cylindrical capacitor with plate radii $a$ and $b,$ the potential difference between the plates is $V.$ The electric field between the plates at a radial distance $r$ from axis is

• A. $\frac{V}{r\ln \left(\frac{b}{a}\right)}$
• B. $\frac{V\ln \left(\frac{b}{a}\right)}{r}$
• C. $\frac{V}{r}$
• D. $\frac{V}{\left(b-a\right)}$

Answer 1

The correct option is A $\frac{V}{r\ln \left(\frac{b}{a}\right)}$

$E=\frac{\lambda }{2\pi {\epsilon }_{0}r}$

$\lambda =Q.Area$

$E=\frac{Q.Area}{2\pi {\epsilon }_{0}r}$

$Q=CV$

$C=\frac{2\pi {\epsilon }_0}{\ln \left(b/a\right)}$

$E=\frac{\frac{2\pi {\epsilon }_0}{\ln b/a}.Area.V}{2\pi {\epsilon }_0.r}\frac{E}{A}=\frac{V}{r\ln \left(b/a\right)}$