Air “breaks down” when the electric field strength reaches 3 × 106 N/C, causing a spark. A parallel-plate capacitor is made from two 3.0 cm

Question

Air “breaks down” when the electric field strength reaches 3 × 106 N/C, causing a spark. A parallel-plate capacitor is made from two 3.0 cm × 3.0 cm electrodes.How many electrons must be transferred from one electrode to the other to create a spark between the electrodes?

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Cherry 2 weeks 2021-09-02T06:21:44+00:00 1 Answers 0 views 0

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    2021-09-02T06:23:43+00:00

    Answer:

    1.5\times 10^{11}}

    Explanation:

    We are given that

    Electric field=E=3\times 10^6 N/C

    Dimension of parallel plate capacitor=3 cm\times 3 cm

    Area of parallel plate capacitor=A=3\times 3=9 cm^2=9\times 10^{-4}m^2

    1 cm^2=10^{-4} m^2

    We have to find the number of electrons must be transferred from one electrode to the other to create  a spark between the electrodes.

    E=\frac{Q}{\epsilon_0A}

    Where \epsilon_0=8.85\times 10^{-12}C^2/Nm^2

    Substitute the values

    3\times 10^6=\frac{Q}{8.85\times 10^{-12}\times 9\times 10^{-4}}

    Q=3\times 10^6\times 8.85\times 10^{-12}\times 9\times 10^{-4}}

    Q=2.4\times 10^{-8} C

    We know that

    Q=ne=n\times 1.6\times 10^{-19}

    Where e=1.6\times 10^{-19} C

    n=\frac{Q}{e}=\frac{2.4\times 10^{-8}}{1.6\times 10^{-19}}=1.5\times 10^{11}}

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