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Question 6 A charged particle moving in a magnetic field will experience a magnetic force. Suppose that the magnetic force experienced by the moving charged particle can be described by the vector field F(x, y) = y't +;x³j. (a) Evaluate F(0,1), F(1,0), F(0,2). F(2,0), F(1,1), F(2,2), F(1,2), F(2,1). (b) Describe F by sketching the vectors from Question 6(a) in the first quadrant plane. (c) Determine if F is a conservative vector field.

Question 6 A charged particle moving in a magnetic field will experience a magnetic force. Suppose that the magnetic force experienced by the moving charged particle can be described by the vector field F(x, y) = y't +;x³j. (a) Evaluate F(0,1), F(1,0), F(0,2). F(2,0), F(1,1), F(2,2), F(1,2), F(2,1). (b) Describe F by sketching the vectors from Question 6(a) in the first quadrant plane. (c) Determine if F is a conservative vector field.

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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neeDed to be solve a,b and c part correctly in one hour please solve correctly
Question 6 A charged particle moving in a magnetic field will experience a magnetic force. Suppose that the magnetic force experienced by the moving charged particle can be described by the vector field F(x, y) = (a) Evaluate F(0,1), F(1,0), F(0,2), F(2,0), F(1,1), F(2,2), F(1,2), F(2,1). (b) Describe F by sketching the vectors from Question 6(a) in the first quadrant plane. (c) Determine if F is a conservative vector field. Given that the charged particle is moving along the straight line from (3, – 3) to (0,3), as represented by the solid line in the figure below. (d) (0, 3) (0, 0) X, (3, -3) Figure Q6(d) Calculate the work done by the magnetic force given by the integral F.dr, where C is the straight line from (3,-3) to (0,3). Now, consider the polygonal region with vertices (0, 3), (0,0) and (3, – 3) as shown in the figure above (the region bounded by the dotted and solid lines), use Green's Theorem to calculate the work done (e) .dr where C is the straight line described in Question 6(d).
Transcribed Image Text:Question 6 A charged particle moving in a magnetic field will experience a magnetic force. Suppose that the magnetic force experienced by the moving charged particle can be described by the vector field F(x, y) = (a) Evaluate F(0,1), F(1,0), F(0,2), F(2,0), F(1,1), F(2,2), F(1,2), F(2,1). (b) Describe F by sketching the vectors from Question 6(a) in the first quadrant plane. (c) Determine if F is a conservative vector field. Given that the charged particle is moving along the straight line from (3, – 3) to (0,3), as represented by the solid line in the figure below. (d) (0, 3) (0, 0) X, (3, -3) Figure Q6(d) Calculate the work done by the magnetic force given by the integral F.dr, where C is the straight line from (3,-3) to (0,3). Now, consider the polygonal region with vertices (0, 3), (0,0) and (3, – 3) as shown in the figure above (the region bounded by the dotted and solid lines), use Green's Theorem to calculate the work done (e) .dr where C is the straight line described in Question 6(d).
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