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20 May, 19:53

The capacitor is now disconnected from the battery, and the plates of the capacitor are then slowly pulled apart until the separation reaches 3d3d. Find the new energy U1U1U_1 of the capacitor after this process.

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  1. 20 May, 20:04
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    U₁ = (ϵAV²) / 6d

    This means that the new energy of the capacitor is (1/3) of the initial energy before the increased separation.

    Explanation:

    The energy stored in a capacitor is given by (1/2) (CV²)

    Energy in the capacitor initially

    U = CV²/2

    V = voltage across the plates of the capacitor

    C = capacitance of the capacitor

    But the capacitance of a capacitor depends on the geometry of the capacitor is given by

    C = ϵA/d

    ϵ = Absolute permissivity of the dielectric material

    A = Cross sectional Area of the capacitor

    d = separation between the capacitor

    So,

    U = CV²/2

    Substituting for C

    U = ϵAV²/2d

    Now, for U₁, the new distance between plates, d₁ = 3d

    U₁ = ϵAV²/2d₁

    U₁ = ϵAV² / (2 (3d))

    U₁ = (ϵAV²) / 6d

    This means that the new energy of the capacitor is (1/3) of the initial energy before the increased separation.
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