2√2r(a) Given that r = xi+yj+zk is a variable point in R³ and a force field F(x, y, z)=TrlFind the work done in moving a particle of mass 2kg from (1,2, -1) to (3,-1, 5)(b) If G(x, y) = (x² - y²)i +5xyj, find [G.dr along the curve C:x=t, y = 2t², 0≤t≤1 andt = sin(u)

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Answered: 2√2r (a) Given that r= xi+yj+zk is a…

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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Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then B(r) = {Bk if R r where r = √x² + y² is the distance to the z-axis and B is a constant that depends on the current strength I and the spacing of the turns of wire. The vector potential for B is A(r) = { }B (-3,2,0) B(-y.x,0) 8 (a) Use Stokes' Theorem to compute the flux of B through a circle in the xy-plane of radius r = 6 R if r < R A dr = (b) Use Stokes' Theorem to compute the circulation of A around the boundary C of a surface lying outside the solenoid. (Use symbolic notation and fractions where needed.) C 2 Br 0
Let (4xy-3x²z²)₁ + (2x²)Ĵ − 2x³ zk = (i) Find a scalar potential for F. (x, y, z) = - note: Answer should have "+C" in it, where C is some constant (ii) Find the work done in moving from (1,1,0) to (2, −1, 1) by the above force field. W= (iii) Solve the differential equation (4xy - 3x²²)dx + 2x²dy - 2x³zdz = 0 ☐ = K, where K is a constant
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2√2r (a) Given that r= xi+yj+zk is a variable point in R³ and a force field F(x, y, z) Find the work done in moving a particle of mass 2kg from (1,2,-1) to (3, -1, 5) Irl 21² 0