What is the mechanical work done in pulling the slab out of the capacitor after disconnecting it from the battery:
Correct answer: A. 1/2 E2C(εr - 1)
- A. 1/2 E2C(εr - 1)
- B. E2C
- C. E2C (εr − 1)
- D. None of these
Explanation
The mechanical work done in pulling the slab out of a disconnected capacitor involves calculating the change in stored energy. When the capacitor is disconnected from the battery, the charge remains constant. The initial energy stored with the dielectric slab can be written as Ui = 1/2 CV2εr, where εr is the relative permittivity of the dielectric. After removing the slab, the capacitance changes, and the final energy is Uf = 1/2 CV2. The work done, which is the change in energy, is ΔU = Uf - Ui = 1/2 CV2(1 - εr). Thus, the correct option, 1/2 E2C(εr - 1), represents this change in energy. The other options incorrectly calculate the energy difference or lack the halving factor.
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