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 vectorin 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 itsinverse is unity.

note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Answered: (b) Derive a relation for V x B in…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.5: Polar Coordinates

Problem 98E

See similar textbooks

Similar questions

Consider the scalar field (image provide). Use gradφ (image provide) to find a unit vector in the direction of gradφ. State how the direction of gradφ relates to surfaces of constant φ(x, y, z).
Prove Stokes theorem for the vector field P over the triangle area bounded by this path by the path indicated by the arrows in the xy planet in the figure.
? Is the vector field protected? Your show. If it is protected, find a potential function for the vector field ?.
Find the flux of the vector field along the Surface given from the parabolic cilinder an the planes
F Is the vector field protected? Your show. If it is protected, find a potential function for the vector field F.
Using Green's Theorem on this vector field problem, compute a) the circulation on the boundary of R in terms of a and b, and b) the outward flux across the boundary of R in terms of a and b.
The angular velocity vector, ω, can be obtained by adding all components of the angular velocities or byA. taking half of the Laplacian form of the vector v.B. taking half of the curl of vector v.C. taking the gradient of vector v.D. solving for the cross product of the vector field and the gradient of v.
Find the unit tangent and unit normal vectors to the space curve (circularhelix) determined by the vector-valued function r(t) =< Sin2t, Cos2t, t>.
What is the gradient of the following scalar function, in spherical coordinates:
Calc 3 - Flux of a vector field over a surface
The vectorfield r^2 shown in (Image 1) Let C be a part of an parabel in the form of y = ax^2 from point A(0,0) to B(1,2) . The given integral is (Image 2) Task is: Find a paramterization of the curve with the use of t, and calculate the integral with the use of definition. Then show that the vectorfield F is conservative, find the potential fucntion and calculate it.
a. Outward flux and area Show that the outward flux of theposition vector field F = xi + yj across any closed curve towhich Green’s Theorem applies is twice the area of the regionenclosed by the curve.b. Let n be the outward unit normal vector to a closed curve towhich Green’s Theorem applies. Show that it is not possiblefor F = x i + y j to be orthogonal to n at every point of C.

SEE MORE QUESTIONS

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Algebra and Trigonometry (MindTap Course List)

Algebra

ISBN:

9781305071742

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Algebra and Trigonometry (MindTap Course List)

Algebra

ISBN:

9781305071742

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

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