Question

A cylindrical capacitor has two co-axial cylinders of length 20 cm and radii 2r and r.Inner cylinder is given a charge 10 $\mu C$ and outer cylinder a charge of -10 $\mu C$.The potential difference between the two cylinders will be.

• A. $\frac{0.1In2}{4\pi {\epsilon }_0}mV$
• B. $\frac{In2}{4\pi {\epsilon }_0}mV$
• C. $\frac{10In2}{4\pi {\epsilon }_0}mV$
• D. $\frac{0.01In2}{4\pi {\epsilon }_0}mV$

Answer 1

The correct option is A $\frac{0.1In2}{4\pi {\epsilon }_0}mV$

Length $=20cm$

radii $=2r,r$

linear cylinder is given a charge $10\mu C$ and outer cylinder a charge $=10\mu C$

The potential difference between the two cylinder will

$W=\frac{\lambda n}{2\pi {ϵ}_0}ln\left(\frac{r_3}{r_1}\right)$

$=\frac{\lambda ln2}{4\pi {ϵ}_0}$

$=\frac{0.1ln2}{4\pi {ϵ}_0}mV$ (from this the previous equation).