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Arisa [49]
3 years ago
7

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

(measured in coulombs per square meter). Find the total charge on the disk.
Physics
1 answer:
maw [93]3 years ago
8 0

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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