(B) Let the charge on the inner sphere be $q$. Since the inner sphere is earthed,its potential $V$ must be zero.The potential at the surface of the in

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(B) Let the charge on the inner sphere be $q$. Since the inner sphere is earthed,its potential $V$ must be zero.The potential at the surface of the inner sphere is due to its own charge $q$ and the charge $Q = 6 \, \mu C$ on the outer shell.The potential $V$ at the inner sphere (radius $r_1 = 1 \, m$) is given by:$V = \frac{k q}{r_1} + \frac{k Q}{r_2} = 0$Substituting the given values $r_1 = 1 \, m$,$r_2 = 3 \, m$,and $Q = 6 \, \mu C$:$\frac{k q}{1} + \frac{k (6)}{3} = 0$$k q + 2k = 0$$q = -2 \, \mu C$Thus,the charge on the inner sphere is $-2 \, \mu C$.

Class 12 Physics Electric Potential and Capacitance Conductor, Electrostatic Shielding, Induced Charge and Charge Redistribution on conductor

Medium

The figure shows a solid conducting sphere of radius $1 \, m$,enclosed by a metallic shell of radius $3 \, m$ such that their centers coincide. If the outer shell is given a charge of $6 \, \mu C$ and the inner sphere is earthed,find the charge on the surface of the inner sphere in $\mu C$.

A
$1$
B
$-2$
C
$4$
D
$6$

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Electric Potential and Capacitance

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Conductor, Electrostatic Shielding, Induced Charge and Charge Redistribution on conductor

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Two metal spheres of radius $R$ and $3R$ have the same surface charge density $\sigma$. If they are brought in contact and then separated, the surface charge density on the smaller and bigger sphere becomes $\sigma_1$ and $\sigma_2$, respectively. The ratio $\frac{\sigma_1}{\sigma_2}$ is:

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$A$ and $B$ are two identical spheres. The charges on them are $7\,\mu C$ and $1\,\mu C$ respectively. Now,both are connected by a wire. Calculate the flow of charge from $A$ to $B$ in $\mu C$.

Medium

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The metal plate on the left in the figure has a charge of $+q$. The metal plate on the right has a charge of $-2q$. What charge will flow to the earth when switch $S$ is closed, given that the middle plate is initially neutral?

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The figure shows a solid conducting sphere of radius $1 \, m$,enclosed by a metallic shell of radius $3 \, m$ such that their centers coincide. If the outer shell is given a charge of $6 \, \mu C$ and the inner sphere is earthed,find the charge on the surface of the inner sphere in $\mu C$.

Similar Questions

$A$ sphere '$1$' with radius $R$ has charge $q$. Sphere '$2$' with radius $3R$ is far from sphere '$1$' and is initially uncharged. If the two spheres are now connected with a thin conducting wire,then the ratio $\frac{\sigma_1}{\sigma_2}$ of the surface charge densities is

Two metal spheres of radius $R$ and $3R$ have the same surface charge density $\sigma$. If they are brought in contact and then separated, the surface charge density on the smaller and bigger sphere becomes $\sigma_1$ and $\sigma_2$, respectively. The ratio $\frac{\sigma_1}{\sigma_2}$ is:

$A$ and $B$ are two identical spheres. The charges on them are $7\,\mu C$ and $1\,\mu C$ respectively. Now,both are connected by a wire. Calculate the flow of charge from $A$ to $B$ in $\mu C$.

The metal plate on the left in the figure has a charge of $+q$. The metal plate on the right has a charge of $-2q$. What charge will flow to the earth when switch $S$ is closed, given that the middle plate is initially neutral?

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