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Arisa [49]
2 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]2 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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Explanation:

The heat required to change the temperature of  steam from 125.5  °C to 100 °C is:

Q_1 = ms_{steam} (125.5^0C - 100^0C) \\ \\ Q_1 = 0.175 \ kg ( 1520 \ J/kg.K ) (25.5^0 \ C) \\ \\ Q_1 = 6783 \ J

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The heat required to change the water at 0°C to ice at 0°C  is:

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Q = Q_1 + Q_2 + Q_3 + Q_4 +Q_5 \\ \\Q = (6788+393750+73255+58450+7132.125)J \\ \\ Q = 539325.125 \ J \\ \\ Q = 5.39*10^5 \ J

b)

The time taken to convert steam from 125 °C to 100°C is:

t_1 = \frac{Q_1}{P} = \frac{6738 \ J}{835 \ W}  = 8.12 \ s

The time taken to convert steam at  100°C to water at  100°C is:

t_2 = \frac{Q_2}{P} =\frac{393750}{834} =471.56 \ s

The time taken to convert water to 100° C to 0° C is:

t_3 = \frac{Q_3}{P} =\frac{73255}{834} = 87.73 \ s

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The time taken to convert ice from 0° C to -19.5° C is:

t_5 = \frac{Q_5}{P} =\frac{7132.125}{834} = 8.55  \ s

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