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(b) Derive a relation for V x B in curvilinear coordinates, where B in curvilinear coordinates. is a vector

(b) Derive a relation for V x B in curvilinear coordinates, where B in curvilinear coordinates. is a vector

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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Do and b just firstly

(a) Define scalar potential. Prove that, in any simply connected region, F =-V@ where p is a scalar function. (b) Derive a relation for Vx B in curvilinear coordinates, where B is a vector in curvilinear coordinates. (a) Explain the terms covariant and contra-variant derivatives. (b) Prove that, in the case of spherical polar coordinates, the product of Jacobian and its inverse is unity.
Transcribed Image Text:(a) Define scalar potential. Prove that, in any simply connected region, F =-V@ where p is a scalar function. (b) Derive a relation for Vx B in curvilinear coordinates, where B is a vector in curvilinear coordinates. (a) Explain the terms covariant and contra-variant derivatives. (b) Prove that, in the case of spherical polar coordinates, the product of Jacobian and its inverse is unity.
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