Express the vector field B = (x^2-y^2)ay + xzaz in sphericalcoordinates at ( 4, 30o, 120o) *Express the vector field B = (x2 – y²)ay + xza, in spherical coordinates at ( 4, 30°, 120°)6.78ar + 0.232ae + 9aØ-3.87ar - 0.332ae + 5aØ-9.87ar + 0.232ae + 6aØO -3.87ar + 0.232ae + aØ

Relation between cartesian and spherical co ordinate system x= r sinθ cosϕ , y = r sinθ sinϕ ,…

Answered: Express the vector field B = (x^2-…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Vectors In Two And Three Dimensions

Section9.FOM: Focus On Modeling: Vectors Fields

Problem 11P

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A particle starts at the point (−4, 0), moves along the x-axis to (4, 0), and then along the semicircle y = 16 − x2 to the starting point. Use Green's Theorem to find the work done on this particle by the force field F(x, y) = 5x, x3 + 3xy2 .
A particle starts at the point (-1, 0), moves along the x-axis to (1, 0), and then along the semicircle y = √(1 - x2 )to the starting point. Use Green's Theorem to find the work done on this particle by the force field F(x, y) = ‹3x, x3 + 3xy2›.
Find the work done by the vector field ⟨4x+yx,x2+6⟩ on a particle moving along the boundary of the rectangle 0≤x≤3,0≤y≤6 in the counterclockwise direction.(The force is measured in newtons, length in meters, work in joules=(newton-meters).) W=____
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If ϕ=3xy+2x2yz−12xz3ϕ=3xy+2x2yz−12xz3, Find ∇×(∇ϕ)The vector field F(x,y)=xi+yjx2+y2F(x,y)=xi+yjx2+y2 is solenoidal what points? Find the divergence at (4,0,0)(4,0,0) for the vector field F(x,y,z)=exsinyi−excosyj+z2kF(x,y,z)=exsin⁡yi−excos⁡yj+z2k Consider the conservative vector field F(x,y,z)=(yz+2x)i+(xz+2y)j+(xy+2z)k.F(x,y,z)=(yz+2x)i+(xz+2y)j+(xy+2z)k. Evaluate ∫cF⋅dr,∫cF⋅dr, c: is a curve starting at (0,0,0)(0,0,0) to (1,1,1).(1,1,1). Use Stoke's theorem to evaluate ∮c(sinzdx−cosxdy+sinydz)∮c(sin⁡zdx−cos⁡xdy+sin⁡ydz) where c is the boundary of the rectangule 0≤x≤π,0≤y≤1,z=3. Determine whether the vector field is conservative. If it is, find a potential function for the vector field. F(x,y,z)=7x6y8z9i+8x7y7z9j+9x7y8z8kF(x,y,z)=7x6y8z9i+8x7y7z9j+9x7y8z8k Given a vector field F(x,y,z)=(3x+z)i+(y2−sinx2z)j+(xz+yex5)k,F(x,y,z)=(3x+z)i+(y2−sin⁡x2z)j+(xz+yex5)k, the divengence theorem value in the region…

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Express the vector field B = (x^2- y^2)ay + xzaz in spherical coordinates at ( 4, 30o, 120o) * Express the vector field B = (x2 – y²)ay + xza, in spherical coordinates at ( 4, 30°, 120°) 6.78ar + 0.232ae + 9aØ -3.87ar - 0.332ae + 5aØ -9.87ar + 0.232ae + 6aØ -3.87ar + 0.232ae + aØ O O