Calculating Work Required to Remove Dielectric Slab from Charged Capacitor

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SUMMARY

The discussion focuses on calculating the work required to remove a dielectric slab from a charged parallel-plate capacitor. The capacitor has a capacitance of 2.19 nF and an initial potential difference of 94 V, with a dielectric constant k of 7.54. The work done is calculated using the formulas W = Ui - Uf, where Ui and Uf represent the initial and final energy stored in the capacitor, respectively. The key takeaway is that when the battery is removed, the charge remains constant, leading to a change in potential difference upon removal of the dielectric slab.

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  • Basic grasp of electrical circuits, particularly the behavior of capacitors when disconnected from a power source.
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This discussion is beneficial for electrical engineers, physics students, and anyone involved in capacitor design or analysis, particularly in understanding the effects of dielectrics on energy storage and work calculations.

srhly
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An isolated capacitor has a dielectric slab k between its two plates. The capacitor is charged by a battery. After the capacitor is charged, the battery is removed. The dielectric slab is then removed. Finally, the capacitor reaches equilibrium. Initially the parallel-plate capacitor has a capacitance of 2.19nF is charged to an initial potential difference of 94 V. The dielectric material has a dielectric constant k = 7.54. What is the magnitude of the work required when the dielectric slab is then removed?

I used:
W= Ui - Uf
U= 0.5CV^2
Uf= (0.5)C(k*Vi)^2
Ui = (0.5)C(Vi)^2

Vi=initial potential difference.

I have tried to double check the math, so I guess I messed up with the formulas. Where did I go wrong?
 
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After charging, the battery is removed hence by displacing the slab the capacitance will change produces change in potential difference between the plates.

In such processes where the battery is disconnected the charge will remain unaltered, not potential difference.
 

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