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12 February, 04:35

A parallel plate capacitor has two plates has a separation d. If I charge it with a + Q and a? Q on the two plates, respectively, what is the electrostatic energy? What is it if I move to 1/2 d?

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  1. 12 February, 08:21
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    Electric energy per unit volume

    = (1 / 2) x ε₀ E²

    Total energy

    = energy per unit volume x volume

    = (1 / 2) x ε₀ E² x A d, A is plate area

    = (1 / 2A) x (ε₀ (σ/ε₀) ² x A² d) [ E is electric field ]

    (1 / 2A) x (ε₀ (σA/ε₀) ² X d)

    (1 / 2A) x (ε₀ (Q/ε₀) ² X d

    = (1 / 2A) x (Q²/ε₀) x d

    So total energy is proportional to d, distance between plates

    if d is changed to d/2

    total energy also becomes half.

    (1 / 2A) x (Q²/ε₀) x d / 2

    (1 / 4A) x (Q²/ε₀) x d

    =
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