A conducting sphere A of radius a,with charge | vedclass

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

Question

(D) Since the shell $B$ is earthed,its potential $V_B = 0$. Due to induction,a charge $-Q$ is induced on the inner surface of shell $B$. For $a \leq r

Vedclass · Accepted Answer

All of the above.

Vedclass · Answer

(D) Since the shell $B$ is earthed,its potential $V_B = 0$. Due to induction,a charge $-Q$ is induced on the inner surface of shell $B$. For $a \leq r \leq b$,the electric field is due to the charge $Q$ on sphere $A$ only: $E = \frac{1}{4\pi \varepsilon_0} \frac{Q}{r^2}$. Thus,option $A$ is correct. The potential at distance $r$ is the sum of potentials due to charge $Q$ on $A$ and induced charge $-Q$ on $B$: $V(r) = \frac{1}{4\pi \varepsilon_0} \frac{Q}{r} + \frac{1}{4\pi \varepsilon_0} \frac{-Q}{b} = \frac{1}{4\pi \varepsilon_0} Q \left( \frac{1}{r} - \frac{1}{b} \right)$. Thus,option $B$ is correct. The potential of sphere $A$ is $V_A = V(a) = \frac{1}{4\pi \varepsilon_0} Q \left( \frac{1}{a} - \frac{1}{b} \right)$. Since $V_B = 0$,the potential difference $V_A - V_B = \frac{1}{4\pi \varepsilon_0} Q \left( \frac{1}{a} - \frac{1}{b} \right)$. Thus,option $C$ is correct. Therefore,all statements are correct.

$A$ conducting sphere $A$ of radius $a$,with charge $Q$,is placed concentrically inside a conducting shell $B$ of radius $b$. $B$ is earthed. $C$ is the common centre of the $A$ and $B$.

Similar Questions

Find the effective capacitance between points $P$ and $Q$ in the circuit shown in the figure in $\mu F$.

$A$ part of a circuit is shown in the figure. If $V_A - V_B = 4 \, V$,then find the charge on the $4 \, \mu F$ capacitor connected to point $A$. (in $, \mu C$)

If an electron enters into a space between the plates of a parallel plate capacitor at an angle $\alpha$ with the plates and leaves at an angle $\beta$ to the plates,the ratio of its kinetic energy while entering the capacitor to that while leaving will be

In the circuit shown in the following figure,the potential difference across the $3 \mu F$ capacitor is: (in $V$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module