Question

A conducting sphere of radius R carries a charge Q. It is enclosed by another concentric spherical shell of radius 2R. Charge from the inner sphere is transferred in infinitesimally small installments to the outer sphere. Calculate the work done in transferring the entire charge from the inner sphere to the outer one.

Answer 1

Answer:

Refer the attachment

Explanation:

Work done equals the change in potential energy. Refer attachment

Answer 2

Answer:

The work exists done in transferring the total charge from the inner sphere to the outer one $&-\frac{Q^{2}}{16 \pi \varepsilon_{0} R}\end{aligned}\end{aligned}$.

Explanation:

The work-energy theorem shows that the ideas of work and energy are equal. In the final part, the object will have a specific amount of kinetic energy (K). At the initial position, the object contains "potential energy", which exists as energy associated with a particular position.

The initial mechanical energy of a system equals the final mechanical energy for a system where no work exists done by non-conservative forces (conservation of mechanical energy principle).

The principle of conservation of mechanical energy: If just conservative forces exist accomplishing work, the whole mechanical energy of a system neither rises nor declines in any process. It remains constant—it exists conserved.

Initial potential energy

$U_{i}=\frac{Q^{2}}{8 \pi \varepsilon_{0} R} .$

Final potential energy

$&U_{f}=\frac{Q^{2}}{8 \pi \varepsilon_{0}(2 R)}$

$W \cdot D=U_{f}-U_{i} &$

$=\frac{Q^{2}}{16 \pi \varepsilon_{0} R}-\frac{Q^{2}}{8 \pi \varepsilon_{0} R}$

$&=-\frac{Q^{2}}{16 \pi \varepsilon_{0} R}\end{aligned}\end{aligned}$

Therefore,  the work exists done in transferring the total charge from the inner sphere to the outer one $&-\frac{Q^{2}}{16 \pi \varepsilon_{0} R}\end{aligned}\end{aligned}$.

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