Electric charge is distributed over the disk x2 + y2 ≤ 4 so that the charge density at (x, y) is rho(x, y) = 4x + 4y + 4×2 + 4y2 (measured i

Question

Electric charge is distributed over the disk x2 + y2 ≤ 4 so that the charge density at (x, y) is rho(x, y) = 4x + 4y + 4×2 + 4y2 (measured in coulombs per square meter). Find the total charge on the disk.

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Neala 2 months 2021-07-27T17:17:02+00:00 1 Answers 6 views 0

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    2021-07-27T17:18:55+00:00

    Answer:

    Q=185.84C

    Explanation:

    We have to take into account the integral

    Q=\int \rho dV

    In this case we have a superficial density in coordinate system.

    Hence, we have for R: x2 + y2 ≤ 4

    Q=\int_{-2}^2\int_{-\sqrt{4-x^2}}^{\sqrt{4-x^2}}\rho dydx

    but, for symmetry:

    Q=4\int_0^2\int_0^{\sqrt{4-x^2}}\rho dydx\\\\Q=4\int_0^2\int_0^{\sqrt{4-x^2}}(4x+4y+4x^2+4y^2) dydx\\\\Q=4\int_0^{2}[4x\sqrt{4-x^2}+2(4-x^2)+4x^2\sqrt{4-x^2}+\frac{4}{3}(4-x^2)^{3/2}]dx\\\\Q=4[46.46]=185.84C

    HOPE THIS HELPS!!

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