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5 February, 03:15

A thin, flat washer is a disk with an outer diameter of 14 cm and a hole in the center with a diameter of 7 cm. The washer has a uniform charge distribution and a total charge of 8 nC. What is the electric field on the axis of the washer at a distance of 33 cm from the center of the washer? (Enter the magnitude of the electric field.)

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  1. 5 February, 03:22
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    2583.9 N/C

    Explanation:

    Parameters given:

    Outer diameter = 14 cm

    Outer radius, R = 7cm = 0.07m

    Inner diameter = 7 cm

    Inner radius, r = 3.5 cm = 0.035m

    Charge of washer = 8 nC = 8 * 10^ (-9) C

    Distance from washer, z = 33 cm = 0.33m

    The electric field due to a washer (hollow disk) is given as:

    E = k * σ * 2π [ 1 - z / (√ (z² + R²) ]

    Where σ = charge per unit area

    σ = q/π (R² - r²)

    σ = 8 * 10^ (-9) / (π * (0.07 - 0.035) ²)

    σ = 2.077 * 10^ (-6) C/m²

    => E = 9 * 10^9 * 2.077 * 10^ (-6) * 2π * [1 - 0.33 / (√ (0.33² + 0.07²) ]

    E = 117.467 * 10^3 * (1 - 0.978)

    E = 117.467 * 10^3 * 0.022

    E = 2583.9 N/C
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