A cylindrical capacitor has two co-axial cyli | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The capacitance $C$ of a cylindrical capacitor is given by the formula: $C = \frac{2 \pi \varepsilon_0 l}{\ln(b/a)}$ where $l = 20 \, cm = 0.2 \,

Vedclass · Accepted Answer

$\frac{0.01 \ln 2}{4 \pi \varepsilon_0} \, V$

Vedclass · Answer

(D) The capacitance $C$ of a cylindrical capacitor is given by the formula: $C = \frac{2 \pi \varepsilon_0 l}{\ln(b/a)}$ where $l = 20 \, cm = 0.2 \, m$,$a = r$,and $b = 2r$. Substituting the values: $C = \frac{2 \pi \varepsilon_0 (0.2)}{\ln(2r/r)} = \frac{0.4 \pi \varepsilon_0}{\ln 2}$. The potential difference $\Delta V$ is given by $\Delta V = \frac{Q}{C}$. Given $Q = 10 \, \mu C = 10 	imes 10^{-6} \, C$. $\Delta V = \frac{10 	imes 10^{-6}}{\frac{0.4 \pi \varepsilon_0}{\ln 2}} = \frac{10 	imes 10^{-6} \ln 2}{0.4 \pi \varepsilon_0}$. $\Delta V = \frac{10^{-5} \ln 2}{0.4 \pi \varepsilon_0} = \frac{10^{-4} \ln 2}{4 \pi \varepsilon_0} = \frac{0.0001 \ln 2}{4 \pi \varepsilon_0} \, V$. Note: The provided options seem to have unit discrepancies or scaling errors. Based on the calculation,the magnitude is $\frac{10^{-4} \ln 2}{4 \pi \varepsilon_0} \, V$.

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

Similar Questions

Two spherical conductors $A$ and $B$ of radii $a$ and $b$ $(b > a)$ are placed in air concentrically. $B$ is given a charge $+Q$ and $A$ is grounded. The equivalent capacitance of this system is:

To increase the charge on the plates of a capacitor means . . . . . . .

The capacitance of a spherical capacitor is $100 \ pF$. If the spacing between the two spheres is $1 \ cm$,then the radius of the inner sphere of the capacitor is: (in $cm$)

Eight drops of mercury of equal radii possessing equal charges combine to form a big drop. Then the capacitance of the bigger drop compared to each individual small drop is ........ $times$.

$A$ cylindrical capacitor has two cylinders of radii $1.4\,cm$ and $1.5\,cm$ and length $15\,cm$. The outer cylinder is earthed and the inner cylinder is given a charge of $3.5\,\mu C$. Determine the capacitance of the system and the potential of the inner cylinder.

Vedclass Test Series

Exam Paper Generator

Online Exam Module