a paraellel plate capacitor consists of 2 large circular sheets of metal separated by 1.53 cm. The electric field energy density betwwen pla

Question

a paraellel plate capacitor consists of 2 large circular sheets of metal separated by 1.53 cm. The electric field energy density betwwen plates is 4.41 J/m3 while the capacitor holds .127 J of potential energy. What is the radius of the circular platyes?

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MichaelMet 3 years 2021-08-25T08:57:58+00:00 1 Answers 9 views 0

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  1. minhkhue
    0
    2021-08-25T08:58:58+00:00
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    Answer:

    The radius of the circular plate is 0.774 m

    Explanation:

    Given;

    distance between the parallel plates, d = 1.53 cm = 0.0153 m

    electric field energy density between plates, U_E  = 4.41 J/m³

    Potential energy of the capacitor, U_c = 0.127 J

    Energy density is given as;

    U_E = \frac{U_c}{V}

    where;

    V is volume

    V = \frac{U_c}{U_E} = \frac{0.127}{4.41} = 0.0288 \ m^3

    Volume is given as;

    V = Ad

    where;

    A is area

    A = V / d

    A = (0.0288) / (0.0153)

    A = 1.882 m²

    Area of circular plate is given as;

    A = πr²

    where;

    r is the radius of the circular plate

    r = \sqrt{\frac{A}{\pi} } \\\\r = \sqrt{\frac{1.882}{\pi}}\\\\r = 0.774 \ m

    Therefore, the radius of the circular plate is 0.774 m

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