To prove: That F ( x , y , z ) = 〈 2 y − 1 , 3 z 2 , 2 x y 〉 has a potential function. Find a potential function of this vector field.

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Answer 1

Question

Chapter 18.3, Problem 42E

To determine

To prove:

That $F (x, y, z) = 〈 2 y - 1, 3 z^{2}, 2 x y 〉$ has a potential function.

Find a potential function of this vector field.

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For scalar functions u and v, show that B= (Vu) × (Vv) is solenoidal and that 1 . (uVv - υVu) 2 A is a vector potential for B, i.e. B = V×A.

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Find a potential function of the vector field. F(x,y) = (3x²y + 1, x³+2y) Do not guess, show all steps.

Answer 2

Question

Chapter 18.3, Problem 42E

To determine

To prove:

That $F (x, y, z) = 〈 2 y - 1, 3 z^{2}, 2 x y 〉$ has a potential function.

Find a potential function of this vector field.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 18.3, Problem 42E

To determine

To prove:

That $F (x, y, z) = 〈 2 y - 1, 3 z^{2}, 2 x y 〉$ has a potential function.

Find a potential function of this vector field.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 18.3, Problem 42E

To determine

To prove:

That $F (x, y, z) = 〈 2 y - 1, 3 z^{2}, 2 x y 〉$ has a potential function.

Find a potential function of this vector field.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 18.3, Problem 42E

To determine

To prove:

That $F (x, y, z) = 〈 2 y - 1, 3 z^{2}, 2 x y 〉$ has a potential function.

Find a potential function of this vector field.

Answer 6

Chapter 18.3, Problem 42E

To determine

To prove:

That $F (x, y, z) = 〈 2 y - 1, 3 z^{2}, 2 x y 〉$ has a potential function.

Find a potential function of this vector field.

Answer 7

Chapter 18.3, Problem 42E

To determine

To prove:

That $F (x, y, z) = 〈 2 y - 1, 3 z^{2}, 2 x y 〉$ has a potential function.

Find a potential function of this vector field.

Answer 8

Expert Solution & Answer

Answer 9

Expert Solution & Answer

Answer 10

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Answer 11

Ch. 18.1 - Prob. 1PQ Ch. 18.1 - Prob. 2PQ Ch. 18.1 - Prob. 3PQ Ch. 18.1 - Prob. 4PQ Ch. 18.1 - Prob. 5PQ Ch. 18.1 - Prob. 1E Ch. 18.1 - Prob. 2E Ch. 18.1 - Prob. 3E Ch. 18.1 - Prob. 4E Ch. 18.1 - Prob. 5E

To prove: That F ( x , y , z ) = 〈 2 y − 1 , 3 z 2 , 2 x y 〉 has a potential function. Find a potential function of this vector field.

Solution Summary: The author explains that if the vector field's curl is zero, it has a potential function.

Videos

To prove:

That $F (x, y, z) = 〈 2 y - 1, 3 z^{2}, 2 x y 〉$ has a potential function.

Find a potential function of this vector field.

Want to see the full answer?

Chapter 18 Solutions

To prove: That F ( x , y , z ) = 〈 2 y − 1 , 3 z 2 , 2 x y 〉 has a potential function. Find a potential function of this vector field.

Solution Summary: The author explains that if the vector field's curl is zero, it has a potential function.

Videos

To prove: That F(x,y,z)=〈2y−1,3z2,2xy〉 has a potential function. Find a potential function of this vector field.

Want to see the full answer?

Chapter 18 Solutions

To prove:

That $F (x, y, z) = 〈 2 y - 1, 3 z^{2}, 2 x y 〉$ has a potential function.

Find a potential function of this vector field.