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The magnetic field B due to a small current loop (which is placed at the origin) is called a magnetic dipole. Let 1/2 P = (x² + y² + z²) ¹¹². For p large, B = curl(A), where A y = (-₁0) Current loop (a) Let C be a horizontal circle of radius R with center (0, 0, c), and parameterization c(t) where c is large. Which of the following correctly explains why A is tangent to C? A(c(t)) = R cos(t) R sin(t) .0 and c'(t)= (-R sin(t), R cos(t), 0)

The magnetic field B due to a small current loop (which is placed at the origin) is called a magnetic dipole. Let 1/2 P = (x² + y² + z²) ¹¹². For p large, B = curl(A), where A y = (-₁0) Current loop (a) Let C be a horizontal circle of radius R with center (0, 0, c), and parameterization c(t) where c is large. Which of the following correctly explains why A is tangent to C? A(c(t)) = R cos(t) R sin(t) .0 and c'(t)= (-R sin(t), R cos(t), 0)

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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17.2 #10

This is just one big question! I need help w/ part b. Please and Thank you!

The magnetic field B due to a small current loop (which is placed at the origin) is called a magnetic dipole. Let 1/2 P = = (x² + y² + z²)¹¹2. For p large, B = curl(A), where A = y X (-³²²₁0) R Current loop (a) Let C be a horizontal circle of radius R with center (0, 0, c), and parameterization c(t) where c is large. Which of the following correctly explains why A is tangent to C? A(c(t)) = (-R R cos(t) R sin(t) 0) and c' (t) = (-R sin(t), R cos(t), 0) So, A(c(t)) c' (t) = 0. Therefore, A is perpendicular to c' (t) and tangent to C. R sin(t) R cos(t) A(C(1)) = (-¹ 2.0) and c'(t) = (R cos(t), -R sin(t), 0)
Transcribed Image Text:The magnetic field B due to a small current loop (which is placed at the origin) is called a magnetic dipole. Let 1/2 P = = (x² + y² + z²)¹¹2. For p large, B = curl(A), where A = y X (-³²²₁0) R Current loop (a) Let C be a horizontal circle of radius R with center (0, 0, c), and parameterization c(t) where c is large. Which of the following correctly explains why A is tangent to C? A(c(t)) = (-R R cos(t) R sin(t) 0) and c' (t) = (-R sin(t), R cos(t), 0) So, A(c(t)) c' (t) = 0. Therefore, A is perpendicular to c' (t) and tangent to C. R sin(t) R cos(t) A(C(1)) = (-¹ 2.0) and c'(t) = (R cos(t), -R sin(t), 0)
So, A(c(t)) · c' (t) = 0. Therefore, A is perpendicular to c' (t) and tangent to C. . A(c(t)) = So, A(c(t)) = So, A(c(t)) c' (t) = 0. Therefore, A is perpendicular to c' (t) and tangent to C. =(- R sin(t) R cos(t) p3 A(c(t)) = [B. So, A(c(t)) B. dS A(c(t)) = = ( R sin(t) R cos(t) c'(t). Therefore, A is parallel to c' (t) and tangent to C. =(-· -c'(t). Therefore, A is parallel to c' (t) and tangent to C. Incorrect and c'(t) = (R cos(t), - R sin(t), 0) Rcos(t) R sin(t) (b) Suppose that R = 3 and c = 800. Use Stokes' Theorem to calculate the flux of B through C. (Use decimal notation. Round your answer to eight decimal places.) 6.28318531 and c'(t)= (-R sin(t), R cos(t), 0) (0) and c' (t) = (R cos(t), - R sin(t), 0)
Transcribed Image Text:So, A(c(t)) · c' (t) = 0. Therefore, A is perpendicular to c' (t) and tangent to C. . A(c(t)) = So, A(c(t)) = So, A(c(t)) c' (t) = 0. Therefore, A is perpendicular to c' (t) and tangent to C. =(- R sin(t) R cos(t) p3 A(c(t)) = [B. So, A(c(t)) B. dS A(c(t)) = = ( R sin(t) R cos(t) c'(t). Therefore, A is parallel to c' (t) and tangent to C. =(-· -c'(t). Therefore, A is parallel to c' (t) and tangent to C. Incorrect and c'(t) = (R cos(t), - R sin(t), 0) Rcos(t) R sin(t) (b) Suppose that R = 3 and c = 800. Use Stokes' Theorem to calculate the flux of B through C. (Use decimal notation. Round your answer to eight decimal places.) 6.28318531 and c'(t)= (-R sin(t), R cos(t), 0) (0) and c' (t) = (R cos(t), - R sin(t), 0)
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