(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

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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 $\mu C$.

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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$A$ charge $q$ is distributed uniformly on the surface of a sphere of radius $R$. It is covered by a concentric hollow conducting sphere of radius $2R$. What will be the charge on the outer surface of the hollow sphere if it is earthed?

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Two conducting spheres $A$ and $B$ have radii $1 \, mm$ and $2 \, mm$ respectively and are charged. They are placed at a distance of $5 \, cm$. When they are connected by a conducting wire,the ratio of the electric field intensities on their surfaces at equilibrium is:

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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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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 $\mu C$.

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$A$ charge of $Q$ coulomb is placed on a solid piece of metal of irregular shape. The charge will distribute itself:

The figure shows three concentric metallic spherical shells. The outermost shell has charge $q_2$,the innermost shell has charge $q_1$,and the middle shell is uncharged. The charge appearing on the inner surface of the outermost shell is

$A$ charge $q$ is distributed uniformly on the surface of a sphere of radius $R$. It is covered by a concentric hollow conducting sphere of radius $2R$. What will be the charge on the outer surface of the hollow sphere if it is earthed?

Two conducting spheres $A$ and $B$ have radii $1 \, mm$ and $2 \, mm$ respectively and are charged. They are placed at a distance of $5 \, cm$. When they are connected by a conducting wire,the ratio of the electric field intensities on their surfaces at equilibrium 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:

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