(a) Suppose that a black hole has magnetic field F = (2a* + e" sin(2), y³ + xe*, 2z³ + e" cos(z) + 3zy²), and that the surface of the black hole is a sphere of radius 5 with an outward orientation. Compute the magnetic flux across the black hole.

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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(a) Suppose that a black hole has magnetic field
F = (2a
+ e" sin(z), y³ + re" , 22³ + e" cos(z) + 3zy?),
and that the surface of the black hole is a sphere of radius 5 with an outward orientation. Compute the magnetic flux
across the black hole.
(b) The Great Stellated Dodecahedron is the solid E shown below. It has a volume of 15. Let S denote the
boundary of E. If F is the vector field F = (z²y+ 2x, e" sin(z) – Y, xª + z) what is the flux of F through E?
-
Transcribed Image Text:(a) Suppose that a black hole has magnetic field F = (2a + e" sin(z), y³ + re" , 22³ + e" cos(z) + 3zy?), and that the surface of the black hole is a sphere of radius 5 with an outward orientation. Compute the magnetic flux across the black hole. (b) The Great Stellated Dodecahedron is the solid E shown below. It has a volume of 15. Let S denote the boundary of E. If F is the vector field F = (z²y+ 2x, e" sin(z) – Y, xª + z) what is the flux of F through E? -
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