Some Applications: 4. (Electromagnetics) If electric charge is distributed over a region D with charge density o(x, y), the total charge is given by o(x, y) dA. Suppose electric charge is distributed over the rectangle 0 < x < 5, 2 < y < 5 so that the charge density at (x, y) is o(x, y) = 2x + 4y (measured in coulombs per square meter). Find the total charge on the rectangle. 1
Some Applications: 4. (Electromagnetics) If electric charge is distributed over a region D with charge density o(x, y), the total charge is given by o(x, y) dA. Suppose electric charge is distributed over the rectangle 0 < x < 5, 2 < y < 5 so that the charge density at (x, y) is o(x, y) = 2x + 4y (measured in coulombs per square meter). Find the total charge on the rectangle. 1
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Transcribed Image Text:5. (Physics) The mass of a region D with density function 8(x, y) is given by
| 5(x, y)dA.
Suppose a circular metal disk of radius 3 lies in the ry-plane with its center at the origin. At a
1
distance r from the origin, the density of the metal per unit area is ổ =
Find the total mass
r2 +1
of the disk.
Transcribed Image Text:Some Applications:
4. (Electromagnetics) If electric charge is distributed over a region D with charge density o(x, y), the
total charge is given by
o(x, y) dA.
Suppose electric charge is distributed over the rectangle 0 < x < 5, 2 < y < 5 so that the charge
density at (x, y) is o(x, y) = 2x + 4y (measured in coulombs per square meter). Find the total charge
on the rectangle.
1
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