Two concentric spherical shells A and B of ra | vedclass

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

Question

(A) The capacitance $C$ of a spherical capacitor with inner radius $a$ and outer radius $b$ is given by the formula $C = 4\pi \varepsilon_0 \frac{ab}{

Vedclass · Accepted Answer

$4\pi \varepsilon_0 \left( \frac{ab}{b - a} \right)$

Vedclass · Answer

(A) The capacitance $C$ of a spherical capacitor with inner radius $a$ and outer radius $b$ is given by the formula $C = 4\pi \varepsilon_0 \frac{ab}{b - a}$.Since shell $A$ is grounded,its potential $V_A = 0$.The potential of shell $B$ is $V_B = \frac{1}{4\pi \varepsilon_0} \frac{Q}{b} + \frac{1}{4\pi \varepsilon_0} \frac{q_A}{b}$,where $q_A$ is the induced charge on shell $A$.However,for a grounded inner shell,the capacitance is defined as the ratio of the charge on the outer shell to the potential difference between the shells.The potential difference is $V = V_B - V_A = \frac{Q}{4\pi \varepsilon_0} \left( \frac{1}{a} - \frac{1}{b} \right)$.Thus,$C = \frac{Q}{V} = \frac{4\pi \varepsilon_0}{\frac{1}{a} - \frac{1}{b}} = 4\pi \varepsilon_0 \frac{ab}{b - a}$.

Two concentric spherical shells $A$ and $B$ of radii $a$ and $b$ $(b > a)$ are placed in air. Shell $B$ is given a charge $+Q$ and shell $A$ is grounded. What is the capacitance of the system?

Similar Questions

$A$ drop of capacitance $1 \ \mu F$ is divided into $8$ identical drops. The capacitance of each small drop is .... $\mu F$.

The graph shows the variation of voltage $V$ across the plates of two capacitors $A$ and $B$ versus the charge $Q$ stored in them. Then:

For the shown situation,in the steady state condition,the ratio of the charge stored in the first capacitor to the charge stored in the $n^{th}$ capacitor is:

The respective radii of the two spheres of a spherical condenser are $12 \; cm$ and $9 \; cm$. The dielectric constant of the medium between them is $6$. The capacity of the condenser will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module