(B) Initial potential energy of the system $(U_i)$: $U_i = U_{\text{sphere}} + U_{\text{shell}} + U_{\text{interaction}}$ $U_i = \frac{KQ^2}{2a} + \fr

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(B) Initial potential energy of the system $(U_i)$: $U_i = U_{\text{sphere}} + U_{\text{shell}} + U_{\text{interaction}}$ $U_i = \frac{KQ^2}{2a} + \frac{KQ^2}{2(2a)} + \frac{KQ \cdot Q}{2a} = \frac{KQ^2}{2a} + \frac{KQ^2}{4a} + \frac{KQ^2}{2a} = \frac{5KQ^2}{4a}$ When connected, the total charge $2Q$ resides on the outer shell because the inner sphere is at a higher potential. Final potential energy of the system $(U_f)$: $U_f = \frac{K(2Q)^2}{2(2a)} = \frac{4KQ^2}{4a} = \frac{KQ^2}{a}$ Heat produced $(H)$ = $U_i - U_f$ $H = \frac{5KQ^2}{4a} - \frac{KQ^2}{a} = \frac{KQ^2}{4a}$

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

Difficult

The figure shows a solid metal sphere of radius $a$ surrounded by a concentric thin metal shell of radius $2a$. Initially, both have charges $Q$ each. When the two are connected by a conducting wire as shown in the figure, the amount of heat produced in this process will be:

A
$\frac{KQ^2}{2a}$
B
$\frac{KQ^2}{4a}$
C
$\frac{KQ^2}{6a}$
D
$\frac{KQ^2}{8a}$

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Class 12 Questions

Class 12

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Chapter

Electrostatic Potential and Capacitance

Subtopic

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

Which of the following statements is always true for a charged conductor?
$(1)$ The electric field just outside the surface is parallel to the surface.
$(2)$ $E_{in} = 0$
$(3)$ Electric field lines are perpendicular to the equipotential surface.

Medium

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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:

DifficultMHT CET 2026

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Consider a finite insulated,uncharged conductor placed near a finite positively charged conductor. The uncharged body must have a potential

DifficultJEE MAIN 2013

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Prove that,if an insulated,uncharged conductor is placed near a charged conductor and no other conductors are present,the uncharged body must be intermediate in potential between that of the charged body and that of infinity.

Medium

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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:

DifficultJEE MAIN 2025

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The figure shows a solid metal sphere of radius $a$ surrounded by a concentric thin metal shell of radius $2a$. Initially, both have charges $Q$ each. When the two are connected by a conducting wire as shown in the figure, the amount of heat produced in this process will be:

Similar Questions

Which of the following statements is always true for a charged conductor?$(1)$ The electric field just outside the surface is parallel to the surface.$(2)$ $E_{in} = 0$$(3)$ Electric field lines are perpendicular to the equipotential surface.

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:

Consider a finite insulated,uncharged conductor placed near a finite positively charged conductor. The uncharged body must have a potential

Prove that,if an insulated,uncharged conductor is placed near a charged conductor and no other conductors are present,the uncharged body must be intermediate in potential between that of the charged body and that of infinity.

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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Which of the following statements is always true for a charged conductor?
$(1)$ The electric field just outside the surface is parallel to the surface.
$(2)$ $E_{in} = 0$
$(3)$ Electric field lines are perpendicular to the equipotential surface.