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5. The following equation describes a portion of a sphere of radius 2 (x, y, z) = (2 cos 0 sin o, 2 sin 0 sin ø, 2 cos o) where 0 < 0 < 2m and 0 < ø < %3D a. Find the surface area of this portion of the sphere. b. If electric charge is distributed over this surface and has a charge density of ð = z coulombs/m², then the total amount of charge on this surface is Sls z dS. Calculate this integral. %3D

5. The following equation describes a portion of a sphere of radius 2 (x, y, z) = (2 cos 0 sin o, 2 sin 0 sin ø, 2 cos o) where 0 < 0 < 2m and 0 < ø < %3D a. Find the surface area of this portion of the sphere. b. If electric charge is distributed over this surface and has a charge density of ð = z coulombs/m², then the total amount of charge on this surface is Sls z dS. Calculate this integral. %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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5. The following equation describes a portion of a sphere of radius 2 (x, y, z) = (2 cos e sin o, 2 sin o sin ø, 2 cos o) T where 0 < 0 < 2m and 0 < ø< 3. %3D a. Find the surface area of this portion of the sphere. b. If electric charge is distributed over this surface and has a charge density of 8 = coulombs/m², then the total amount of charge on this surface is Slsz dS. Calculate this integral.
Transcribed Image Text:5. The following equation describes a portion of a sphere of radius 2 (x, y, z) = (2 cos e sin o, 2 sin o sin ø, 2 cos o) T where 0 < 0 < 2m and 0 < ø< 3. %3D a. Find the surface area of this portion of the sphere. b. If electric charge is distributed over this surface and has a charge density of 8 = coulombs/m², then the total amount of charge on this surface is Slsz dS. Calculate this integral.
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